6286:. By setting coefficients that fall below a shrinkage threshold to zero, once the inverse transform is applied, an expectedly small amount of signal is lost due to the sparsity assumption. The larger coefficients are expected to primarily represent signal due to sparsity, and statistically very little of the signal, albeit the majority of the noise, is expected to be represented in such lower magnitude coefficients... therefore the zeroing-out operation is expected to remove most of the noise and not much signal. Typically, the above-threshold coefficients are not modified during this process. Some algorithms for wavelet-based denoising may attenuate larger coefficients as well, based on a statistical estimate of the amount of noise expected to be removed by such an attenuation.
5312:. This, then, requires an infinite number of Fourier coefficients, which is not practical for many applications, such as compression. Wavelets are more useful for describing these signals with discontinuities because of their time-localized behavior (both Fourier and wavelet transforms are frequency-localized, but wavelets have an additional time-localization property). Because of this, many types of signals in practice may be non-sparse in the Fourier domain, but very sparse in the wavelet domain. This is particularly useful in signal reconstruction, especially in the recently popular field of
10681:
4729:
517:
1347:
535:
10667:
5444:
499:
199:
51:
10705:
10693:
8235:
4768:(FFT). This computational advantage is not inherent to the transform, but reflects the choice of a logarithmic division of frequency, in contrast to the equally spaced frequency divisions of the FFT which uses the same basis functions as the discrete Fourier transform (DFT). This complexity only applies when the filter size has no relation to the signal size. A wavelet without
3081:
For practical applications, and for efficiency reasons, one prefers continuously differentiable functions with compact support as mother (prototype) wavelet (functions). However, to satisfy analytical requirements (in the continuous WT) and in general for theoretical reasons, one chooses the wavelet
3072:
For processing temporal signals in real time, it is essential that the wavelet filters do not access signal values from the future as well as that minimal temporal latencies can be obtained. Time-causal wavelets representations have been developed by Szu et al and
Lindeberg, with the latter method
5232:
Fractional wavelet transform (FRWT) is a generalization of the classical wavelet transform in the fractional
Fourier transform domains. This transform is capable of providing the time- and fractional-domain information simultaneously and representing signals in the time-fractional-frequency plane.
4841:
The wavelet function is in effect a band-pass filter and scaling that for each level halves its bandwidth. This creates the problem that in order to cover the entire spectrum, an infinite number of levels would be required. The scaling function filters the lowest level of the transform and ensures
4716:
A given resolution cell's time-bandwidth product may not be exceeded with the STFT. All STFT basis elements maintain a uniform spectral and temporal support for all temporal shifts or offsets, thereby attaining an equal resolution in time for lower and higher frequencies. The resolution is purely
1354:
In any discretised wavelet transform, there are only a finite number of wavelet coefficients for each bounded rectangular region in the upper halfplane. Still, each coefficient requires the evaluation of an integral. In special situations this numerical complexity can be avoided if the scaled and
42:
that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the number and direction of its pulses. Wavelets are imbued with specific properties that make them useful for
7434:
Wavelets are actively used to solve a wide range of image processing problems in various fields of science and technology, e.g., image denoising, reconstruction, analysis, and video analysis and processing. Wavelet processing methods are based on the discrete wavelet transform using 1D digital
3704:
These functions are often incorrectly referred to as the basis functions of the (continuous) transform. In fact, as in the continuous
Fourier transform, there is no basis in the continuous wavelet transform. Time-frequency interpretation uses a subtly different formulation (after Delprat).
4322:
5107:(CWTs). Note that both DWT and CWT are continuous-time (analog) transforms. They can be used to represent continuous-time (analog) signals. CWTs operate over every possible scale and translation whereas DWTs use a specific subset of scale and translation values or representation grid.
299:
of
Fourier analysis respective sampling theory: given a signal with some event in it, one cannot assign simultaneously an exact time and frequency response scale to that event. The product of the uncertainties of time and frequency response scale has a lower bound. Thus, in the
5271:
A related use is for smoothing/denoising data based on wavelet coefficient thresholding, also called wavelet shrinkage. By adaptively thresholding the wavelet coefficients that correspond to undesired frequency components smoothing and/or denoising operations can be performed.
983:
It is computationally impossible to analyze a signal using all wavelet coefficients, so one may wonder if it is sufficient to pick a discrete subset of the upper halfplane to be able to reconstruct a signal from the corresponding wavelet coefficients. One such system is the
1714:
1891:
1552:
5075:
into different scale components. Usually one can assign a frequency range to each scale component. Each scale component can then be studied with a resolution that matches its scale. A wavelet transform is the representation of a function by wavelets. The wavelets are
4593:
3823:
4724:
properties enables large temporal supports for lower frequencies while maintaining short temporal widths for higher frequencies by the scaling properties of the wavelet transform. This property extends conventional time-frequency analysis into time-scale analysis.
1265:
485:
5307:
Often, signals can be represented well as a sum of sinusoids. However, consider a non-continuous signal with an abrupt discontinuity; this signal can still be represented as a sum of sinusoids, but requires an infinite number, which is an observation known as
2738:
956:
66:
with a signal created from the recording of a melody, then the resulting signal would be useful for determining when the middle C note appeared in the song. Mathematically, a wavelet correlates with a signal if a portion of the signal is similar.
78:
and images. Sets of wavelets are needed to analyze data fully. "Complementary" wavelets decompose a signal without gaps or overlaps so that the decomposition process is mathematically reversible. Thus, sets of complementary wavelets are useful in
6054:
304:
of a continuous wavelet transform of this signal, such an event marks an entire region in the time-scale plane, instead of just one point. Also, discrete wavelet bases may be considered in the context of other forms of the uncertainty principle.
1134:
2918:
6351:
datasets at different timescale averred that wavelet based multi-scale analysis of climatic processes holds the promise of better understanding the system dynamics that may be missed when processes are analyzed at one timescale only
4169:
804:
643:
282:
of dyadic (octave band) configuration is a wavelet approximation to that signal. The coefficients of such a filter bank are called the shift and scaling coefficients in wavelets nomenclature. These filterbanks may contain either
3674:
7391:
TomĂĄs, R., Li, Z., Lopez-Sanchez, J.M., Liu, P. & Singleton, A. 2016. Using wavelet tools to analyse seasonal variations from InSAR time-series data: a case study of the
Huangtupo landslide. Landslides, 13, 437-450, doi:
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2406:
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1397:
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358:
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2315:
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5865:
3148:
5603:
2592:
4637:
3372:
812:
3063:
5264:), and the same frame functions (except for conjugation in the case of complex wavelets) are used for both analysis and synthesis, i.e., in both the forward and inverse transform. For details see
3714:
1324:
3462:(see there for exact statement), the mother wavelet must satisfy an admissibility criterion (loosely speaking, a kind of half-differentiability) in order to get a stably invertible transform.
1967:
343:
The frequency bands or subspaces (sub-bands) are scaled versions of a subspace at scale 1. This subspace in turn is in most situations generated by the shifts of one generating function Ï in
2240:
2186:
8257:
6191:
1023:
1391:
4-tap wavelet. Note that not every orthonormal discrete wavelet basis can be associated to a multiresolution analysis; for example, the Journe wavelet admits no multiresolution analysis.
4038:
2776:
6334:
5705:
5179:, giving rise to a continuous transform space that is a function of time, scale, and frequency. The CWT is a two-dimensional slice through the resulting 3d time-scale-frequency volume.
2053:
2132:
4674:
6649:
Wireless
Communications: Principles and Practice, Prentice Hall communications engineering and emerging technologies series, T. S. Rappaport, Prentice Hall, 2002, p. 126.
5084:
copies (known as "daughter wavelets") of a finite-length or fast-decaying oscillating waveform (known as the "mother wavelet"). Wavelet transforms have advantages over traditional
3951:
5320:(STFT) is also localized in time and frequency, but there are often problems with the frequency-time resolution trade-off. Wavelets are better signal representations because of
686:
6284:
6252:
6118:
6086:
559:
7573:
Abbott, Benjamin P.; et al. (LIGO Scientific
Collaboration and Virgo Collaboration) (2016). "Observing gravitational-wave transient GW150914 with minimal assumptions".
5939:
4156:
3588:
2771:
6220:
5777:
5741:
3880:
4073:
8345:
A dictionary of tens of wavelets and wavelet-related terms ending in -let, from activelets to x-lets through bandlets, contourlets, curvelets, noiselets, wedgelets.
5481:
4331:
1768:
1741:
4703:
4458:
5252:
Like some other transforms, wavelet transforms can be used to transform data, then encode the transformed data, resulting in effective compression. For example,
5931:
5911:
5887:
5800:
5625:
5541:
5521:
5501:
3965:(STFT) is similar to the wavelet transform, in that it is also time and frequency localized, but there are issues with the frequency/time resolution trade-off.
119:
3235:
7126:
6422:
5175:
There are a number of generalized transforms of which the wavelet transform is a special case. For example, Yosef Joseph Segman introduced scale into the
3165:
149:, of different points on the wavefront (or, equivalently, each wavelet) that travel by paths of different lengths to the registering surface. Multiple,
4732:
STFT time-frequency atoms (left) and DWT time-scale atoms (right). The time-frequency atoms are four different basis functions used for the STFT (i.e.
7028:
Gall, Didier Le; Tabatabai, Ali J. (1988). "Sub-band coding of digital images using symmetric short kernel filters and arithmetic coding techniques".
3505:
2411:
2245:
3377:
2923:
4317:{\displaystyle E=\int _{-\infty }^{\infty }|\psi (t)|^{2}\,dt={\frac {1}{2\pi }}\int _{-\infty }^{\infty }|{\hat {\psi }}(\omega )|^{2}\,d\omega }
6741:
Akansu, Ali N.; Haddad, Richard A. (1992), Multiresolution Signal
Decomposition: Transforms, Subbands, and Wavelets, Boston, MA: Academic Press,
2486:
2320:
9802:
7449:"Frequency characteristics analysis of pipe-to-soil potential under metro stray current interference using continuous wavelet transform method"
4078:
3317:
10307:
4973:
algorithm, and the Le GallâTabatabai (LGT) 5/3 discrete-time filter bank (developed by Didier Le Gall and Ali J. Tabatabai in 1988) for its
4910:(CWT) in 1975 (originally called the cochlear transform and discovered while studying the reaction of the ear to sound), Pierre Goupillaud,
3001:
8377:
8205:
4736:). The time-scale atoms of the DWT achieve small temporal widths for high frequencies and good temporal widths for low frequencies with a
10457:
7302:
10081:
8722:
5088:
for representing functions that have discontinuities and sharp peaks, and for accurately deconstructing and reconstructing finite, non-
7059:
Said, Amir; Pearlman, William A. (June 1996). "A new fast and efficient image codec based on set partitioning in hierarchical trees".
5189:
An important application area for generalized transforms involves systems in which high frequency resolution is crucial. For example,
6366:
9855:
7494:
Stefano Galli; O. Logvinov (July 2008). "Recent
Developments in the Standardization of Power Line Communications within the IEEE".
4784:) complexity, but the original signal must be sampled logarithmically in time, which is only useful for certain types of signals.)
1709:{\displaystyle W_{m}=\operatorname {span} (\psi _{m,n}:n\in \mathbb {Z} ),{\text{ where }}\psi _{m,n}(t)=2^{-m/2}\psi (2^{-m}t-n).}
8137:
B. Boashash, editor, "Time-Frequency Signal
Analysis and Processing â A Comprehensive Reference", Elsevier Science, Oxford, 2003,
7261:
HĂżtch, M. J.; Snoeck, E.; Kilaas, R. (1998). "Quantitative measurement of displacement and strain fields from HRTEM micrographs".
5805:
3088:
1886:{\displaystyle \{0\}\subset \dots \subset V_{1}\subset V_{0}\subset V_{-1}\subset V_{-2}\subset \dots \subset L^{2}(\mathbb {R} )}
1547:{\displaystyle V_{m}=\operatorname {span} (\phi _{m,n}:n\in \mathbb {Z} ),{\text{ where }}\phi _{m,n}(t)=2^{-m/2}\phi (2^{-m}t-n)}
107:
95:
10294:
3971:
5546:
5327:
This motivates why wavelet transforms are now being adopted for a vast number of applications, often replacing the conventional
1996:
7668:
J. Rafiee et al. Feature extraction of forearm EMG signals for prosthetics, Expert Systems with Applications 38 (2011) 4058â67.
4957:(JPEG) committee chaired by Touradj Ebrahimi (later the JPEG president). In contrast to the DCT algorithm used by the original
4943:
4600:
3968:
In particular, assuming a rectangular window region, one may think of the STFT as a transform with a slightly different kernel
8172:
7677:
J. Rafiee et al. Female sexual responses using signal processing techniques, The Journal of Sexual Medicine 6 (2009) 3086â96.
5299:
OFDM, and wavelet OFDM does not require a guard interval (which usually represents significant overhead in FFT OFDM systems).
5256:
is an image compression standard that uses biorthogonal wavelets. This means that although the frame is overcomplete, it is a
340:> 0. Then, the original signal can be reconstructed by a suitable integration over all the resulting frequency components.
8184:
8068:
6746:
6730:
4588:{\displaystyle {\hat {\sigma }}_{\xi }^{2}={\frac {1}{2\pi E}}\int |\omega -\xi |^{2}|{\hat {\psi }}(\omega )|^{2}\,d\omega }
3818:{\displaystyle {\frac {1}{\sqrt {a}}}\int _{-\infty }^{\infty }\varphi _{a1,b1}(t)\varphi \left({\frac {t-b}{a}}\right)\,dt}
10736:
8717:
8417:
7101:
5229:
applications for intermediate transforms with high frequency resolution (like brushlets and ridgelets) is growing rapidly.
137:
as a collection of individual spherical wavelets. The characteristic bending pattern is most pronounced when a wave from a
1260:{\displaystyle x(t)=\sum _{m\in \mathbb {Z} }\sum _{n\in \mathbb {Z} }\langle x,\,\psi _{m,n}\rangle \cdot \psi _{m,n}(t)}
480:{\displaystyle \psi (t)=2\,\operatorname {sinc} (2t)-\,\operatorname {sinc} (t)={\frac {\sin(2\pi t)-\sin(\pi t)}{\pi t}}}
9321:
8469:
1270:
3488:, which defines the wavelet by a scaling function. This scaling function itself is a solution to a functional equation.
7097:
JPEG2000 Image Compression Fundamentals, Standards and Practice: Image Compression Fundamentals, Standards and Practice
5111:
4676:
and this convolution is with a delta function in Fourier space, resulting in the true Fourier transform of the signal
1904:
320:, a given signal of finite energy is projected on a continuous family of frequency bands (or similar subspaces of the
10104:
9996:
8283:
8164:
8142:
8131:
8112:
8097:
8082:
8060:
8046:
8035:
8020:
8005:
7987:
7969:
7848:
Agarwal, Ankit; Caesar, Levke; Marwan, Norbert; Maheswaran, Rathinasamy; Merz, Bruno; Kurths, JĂŒrgen (19 June 2019).
7229:
7205:
7109:
7012:
6714:
6698:
6389:
6378:
4966:
2191:
2137:
246:
5249:. Thus, DWT approximation is commonly used in engineering and computer science, and the CWT in scientific research.
228:
10709:
10282:
10156:
6126:
5210:
4954:
2733:{\displaystyle L^{2}=V_{j_{0}}\oplus W_{j_{0}}\oplus W_{j_{0}-1}\oplus W_{j_{0}-2}\oplus W_{j_{0}-3}\oplus \cdots }
6867:
The Scientist and Engineer's Guide to Digital Signal Processing By Steven W. Smith, Ph.D. chapter 8 equation 8-1:
336:) ). For instance the signal may be represented on every frequency band of the form for all positive frequencies
10340:
10001:
9746:
9117:
8707:
8320:
7173:
6579:
146:
8055:, "The World According to Wavelets: The Story of a Mathematical Technique in the Making", A K Peters Ltd, 1998,
6292:
5630:
3953:. The main difference in general is that wavelets are localized in both time and frequency whereas the standard
951:{\displaystyle WT_{\psi }\{x\}(a,b)=\langle x,\psi _{a,b}\rangle =\int _{\mathbb {R} }x(t){\psi _{a,b}(t)}\,dt.}
10391:
9603:
9410:
9299:
9257:
8359:
A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity
7402:
Lyakhov, Pavel; Semyonova, Nataliya; Nagornov, Nikolay; Bergerman, Maxim; Abdulsalyamova, Albina (2023-11-14).
7379:
6810:"A time-causal and time-recursive scale-covariant scale-space representation of temporal signals and past time"
4713:. The choice of windowing function will affect the approximation error relative to the true Fourier transform.
3155:
224:
9331:
2081:
10634:
9593:
8496:
8364:
8308:
6922:
6568:
5110:
There are a large number of wavelet transforms each suitable for different applications. For a full list see
2068:
with sampling distance 2 more or less covers the frequency baseband from 0 to 1/2. As orthogonal complement,
296:
260:
130:
7726:
4646:
10185:
10134:
10119:
10109:
9978:
9850:
9817:
9643:
9598:
9428:
8352:
6620:
6558:
6343:
Agarwal et al. proposed wavelet based advanced linear and nonlinear methods to construct and investigate
5317:
5163:
5157:
5151:
5145:
5118:
5104:
4907:
3962:
3902:
3459:
317:
308:
Wavelet transforms are broadly divided into three classes: continuous, discrete and multiresolution-based.
292:
3899:
can be viewed as a special case of the continuous wavelet transform with the choice of the mother wavelet
10697:
10529:
10330:
10254:
9555:
9309:
8978:
8442:
8303:
7791:
Agarwal, Ankit; Marwan, Norbert; Rathinasamy, Maheswaran; Merz, Bruno; Kurths, JĂŒrgen (13 October 2017).
7725:
Agarwal, Ankit; Maheswaran, Rathinasamy; Marwan, Norbert; Caesar, Levke; Kurths, JĂŒrgen (November 2018).
6491:
6344:
7793:"Multi-scale event synchronization analysis for unravelling climate processes: a wavelet-based approach"
7690:
Rafiee, J.; Tse, Peter W. (2009). "Use of autocorrelation in wavelet coefficients for fault diagnosis".
6659:
Ricker, Norman (1953). "Wavelet Contraction, Wavelet Expansion, and the Control of Seismic Resolution".
5435:
representation and Gaussian derivative operators is regarded as a canonical multi-scale representation.
978:
83:/decompression algorithms, where it is desirable to recover the original information with minimal loss.
10741:
10414:
10386:
10381:
10129:
9888:
9794:
9774:
9682:
9393:
9211:
8694:
8566:
7344:
Shi, J.; Zhang, N.-T.; Liu, X.-P. (2011). "A novel fractional wavelet transform and its applications".
6976:
6548:
6049:{\displaystyle p\ \sim \ a{\mathcal {N}}(0,\,\sigma _{1}^{2})+(1-a){\mathcal {N}}(0,\,\sigma _{2}^{2})}
5222:
5124:
5100:
4962:
4939:
3466:
3159:
91:
74:
As a mathematical tool, wavelets can be used to extract information from many kinds of data, including
8298:
7448:
1129:{\displaystyle \psi _{m,n}(t)={\frac {1}{\sqrt {a^{m}}}}\psi \left({\frac {t-nba^{m}}{a^{m}}}\right).}
10146:
9914:
9635:
9560:
9489:
9418:
9338:
9326:
9196:
9184:
9177:
8885:
8606:
8361:
provides a tutorial on two-dimensional oriented wavelets and related geometric multiscale transforms.
6966:
6257:
6225:
6091:
6059:
288:
3314:
Being in this space ensures that one can formulate the conditions of zero mean and square norm one:
2913:{\displaystyle S=\sum _{k}c_{j_{0},k}\phi _{j_{0},k}+\sum _{j\leq j_{0}}\sum _{k}d_{j,k}\psi _{j,k}}
259:
Wavelet theory is applicable to several subjects. All wavelet transforms may be considered forms of
10629:
10396:
10259:
9944:
9909:
9873:
9658:
9100:
9009:
8968:
8880:
8571:
8410:
8265:
8261:
8245:
6773:
Szu, Harold H.; Telfer, Brian A.; Lohmann, Adolf W. (1992). "Causal analytical wavelet transform".
6590:
5321:
5284:
4816:
4721:
3485:
1894:
1356:
220:
209:
8342:
8328:
by Gilbert Strang, American Scientist 82 (1994) 250â255. (A very short and excellent introduction)
7530:
Wotherspoon, T.; et., al. (2009). "Adaptation to the edge of chaos with random-wavelet feedback".
5213:
are capable of providing digital images with picometer-scale information on atomic periodicity in
4922:(1983), the Le GallâTabatabai (LGT) 5/3-taps non-orthogonal filter bank with linear phase (1988),
169:
has been used for decades in digital signal processing and exploration geophysics. The equivalent
10538:
10151:
10091:
10028:
9666:
9650:
9388:
9250:
9240:
9090:
9004:
7447:
Dong, Liang; Zhang, Shaohua; Gan, Tiansiyu; Qiu, Yan; Song, Qinfeng; Zhao, Yongtao (2023-12-01).
6511:
6348:
5261:
4801:
4134:
284:
213:
111:
2743:
10576:
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10299:
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9991:
9878:
8875:
8772:
8679:
8558:
8457:
5376:
5296:
5130:
5081:
4887:
The development of wavelets can be linked to several separate trains of thought, starting with
4819:
of the low pass, and reconstruction filters are the time reverse of the decomposition filters.
4765:
3491:
In most situations it is useful to restrict Ï to be a continuous function with a higher number
2579:
7916:
7191:
7095:
6998:
6196:
5746:
5710:
5053:
Since the 1990s: Nathalie Delprat, Newland, Amir Said, William A. Pearlman, Touradj Ebrahimi,
4597:
Multiplication with a rectangular window in the time domain corresponds to convolution with a
3856:
10601:
10543:
10486:
10312:
10205:
10114:
9840:
9724:
9583:
9575:
9465:
9457:
9272:
9168:
9146:
9105:
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8983:
8958:
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8812:
8614:
8437:
8052:
6600:
5416:
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4163:
985:
8331:
7289:
Spacing measurements of lattice fringes in HRTEM image using digital darkfield decomposition
4043:
10524:
10099:
10048:
10024:
9986:
9904:
9883:
9835:
9714:
9692:
9661:
9570:
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9398:
9316:
9289:
9245:
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8739:
8619:
8123:
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7804:
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7641:
7594:
7539:
7141:
6782:
6668:
6563:
5454:
5190:
4974:
2578:
for the father wavelet Ï. Both pairs of identities form the basis for the algorithm of the
1746:
1719:
8041:
Martin Vetterli and Jelena KovaÄeviÄ, "Wavelets and Subband Coding", Prentice Hall, 1995,
7932:
7850:"Network-based identification and characterization of teleconnections on different scales"
6479:
4919:
4918:'s formulation of what is now known as the CWT (1982), Jan-Olov Strömberg's early work on
4679:
4443:
3697:; for the discrete WT this pair varies over a discrete subset of it, which is also called
8:
10671:
10596:
10519:
10200:
9964:
9957:
9919:
9827:
9807:
9779:
9512:
9378:
9373:
9363:
9355:
9173:
9134:
9024:
9014:
8923:
8702:
8658:
8576:
8501:
8403:
7654:
7629:
7197:
6889:
6553:
6538:
6459:
5384:
5265:
5218:
5140:
5048:
4876:
4872:
4809:
1388:
1341:
972:
799:{\displaystyle x_{a}(t)=\int _{\mathbb {R} }WT_{\psi }\{x\}(a,b)\cdot \psi _{a,b}(t)\,db}
538:
154:
150:
138:
80:
7865:
7808:
7745:
7703:
7645:
7598:
7543:
7145:
6941:
6836:
6809:
6786:
6672:
5275:
Wavelet transforms are also starting to be used for communication applications. Wavelet
638:{\displaystyle \psi _{a,b}(t)={\frac {1}{\sqrt {a}}}\psi \left({\frac {t-b}{a}}\right),}
311:
10685:
10496:
10350:
10246:
10195:
10071:
9968:
9952:
9929:
9706:
9440:
9423:
9383:
9294:
9189:
9151:
9122:
9082:
9042:
8988:
8905:
8591:
8586:
7993:
7890:
7877:
7849:
7830:
7822:
7773:
7757:
7610:
7584:
7511:
7476:
7361:
7165:
7041:
6904:
6899:
6881:
6693:
Meyer, Yves (1992), Wavelets and Operators, Cambridge, UK: Cambridge University Press,
6610:
6523:
6395:
5916:
5896:
5872:
5785:
5610:
5526:
5506:
5486:
5408:
5388:
5348:
5332:
5313:
5183:
5093:
5077:
2575:
1360:
996:> 0. The corresponding discrete subset of the halfplane consists of all the points (
8074:
7464:
7323:
7274:
5032:
4938:(1990), Nathalie Delprat's time-frequency interpretation of the CWT (1991), Newland's
4899:(1946), which are constructed similarly to wavelets, and applied to similar purposes.
141:
source (such as a laser) encounters a slit/aperture that is comparable in size to its
10731:
10680:
10591:
10561:
10553:
10373:
10364:
10289:
10220:
10076:
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10036:
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9865:
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8895:
8674:
8548:
8180:
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8138:
8127:
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8093:
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8056:
8042:
8031:
8016:
8001:
7983:
7965:
7957:
7895:
7777:
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7614:
7555:
7480:
7468:
7425:
7365:
7225:
7201:
7157:
7105:
7076:
7045:
7008:
6967:"General characteristics and design considerations for temporal subband video coding"
6841:
6742:
6726:
6710:
6709:
Chui, Charles K. (1992), An Introduction to Wavelets, San Diego, CA: Academic Press,
6694:
6449:
5412:
5404:
5368:
5328:
5198:
5089:
5085:
5072:
5066:
5036:
4970:
4923:
4640:
3954:
3896:
3892:
1327:
979:
Discrete wavelet transforms (discrete shift and scale parameters, continuous in time)
268:
126:
44:
7834:
4162:
respectively denote the length and temporal offset of the windowing function. Using
3669:{\displaystyle \psi _{a,b}(t)={1 \over {\sqrt {a}}}\psi \left({t-b \over a}\right).}
2585:
From the multiresolution analysis derives the orthogonal decomposition of the space
10616:
10571:
10335:
10322:
10215:
10190:
10124:
10056:
9934:
9542:
9435:
9368:
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9228:
9047:
8918:
8712:
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8511:
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7885:
7869:
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7707:
7649:
7602:
7547:
7515:
7503:
7460:
7415:
7353:
7270:
7169:
7149:
7068:
7033:
6908:
6894:
6831:
6821:
6790:
6676:
6417:
5428:
5380:
5372:
5309:
5242:
5194:
5176:
4982:
3151:
2058:
8370:
8358:
8316:
1st NJIT Symposium on Wavelets (April 30, 1990) (First Wavelets Conference in USA)
4643:
for short/localized temporal windows. With the continuous-time Fourier transform,
62:
and a short duration of roughly one tenth of a second. If this wavelet were to be
10533:
10277:
10139:
10066:
9741:
9615:
9588:
9565:
9534:
9161:
9156:
9110:
8840:
8491:
8348:
8336:
8253:
8157:
Image Processing and Analysis â Variational, PDE, Wavelet, and Stochastic Methods
7753:
7404:"High-Speed Wavelet Image Processing Using the Winograd Method with Downsampling"
7240:
P. Fraundorf, J. Wang, E. Mandell and M. Rose (2006) Digital darkfield tableaus,
6506:
6469:
6464:
6412:
5424:
5246:
5186:
in which the CWT is also a two dimensional slice through the chirplet transform.
4927:
4773:
4769:
4728:
4710:
2773:
this gives a representation in basis functions of the corresponding subspaces as
264:
170:
10023:
8105:
An Introduction to Wavelets and Other Filtering Methods in Finance and Economics
7711:
7030:
ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing
4815:
For analysis with orthogonal wavelets the high pass filter is calculated as the
10482:
10477:
8940:
8870:
8516:
8325:
7873:
7606:
7037:
7004:
6826:
6630:
6585:
6533:
6501:
6474:
6373:
5890:
5352:
5206:
5136:
5040:
5022:
4990:
4911:
4749:
3470:
520:
326:
182:
103:
87:
7507:
7357:
7220:
P. Hirsch, A. Howie, R. Nicholson, D. W. Pashley and M. J. Whelan (1965/1977)
5007:
4888:
4431:{\displaystyle \sigma _{u}^{2}={\frac {1}{E}}\int |t-u|^{2}|\psi (t)|^{2}\,dt}
10725:
10639:
10606:
10469:
10430:
10241:
10210:
9674:
9628:
9233:
8935:
8762:
8526:
8521:
7881:
7826:
7769:
7761:
7472:
7429:
7080:
6454:
5889:
is orthogonal, the estimation problem amounts to recovery of a signal in iid
5420:
5214:
4849:) can be considered finite in length and is equivalent to the scaling filter
4800:
An orthogonal wavelet is entirely defined by the scaling filter â a low-pass
502:
488:
276:
272:
115:
8152:
8077:, "A wavelet tour of signal processing", 2nd edition, Academic Press, 1999,
7817:
7792:
7153:
4864:
The wavelet only has a time domain representation as the wavelet function Ï(
10581:
10514:
10491:
10406:
9736:
9032:
8930:
8865:
8807:
8792:
8729:
8684:
8171:
Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P. (2007),
8148:
7899:
7575:
7559:
7327:
7319:
7161:
6845:
6496:
6444:
6407:
6401:
5344:
5336:
5014:
5003:
4935:
4903:
4892:
4440:
and the square of the spectral support of the window acting on a frequency
4324:
From this, the square of the temporal support of the window offset by time
2567:{\textstyle \psi (t)={\sqrt {2}}\sum _{n\in \mathbb {Z} }h_{n}\phi (2t-n).}
2401:{\textstyle \phi (t)={\sqrt {2}}\sum _{n\in \mathbb {Z} }g_{n}\phi (2t-n),}
516:
75:
7382:, Physical Communication, Elsevier, vol. 3, issue 1, pp. 1-18, March 2010.
10624:
10586:
10269:
10170:
10032:
9845:
9812:
9304:
9221:
9216:
8860:
8817:
8797:
8777:
8767:
8536:
7630:"Transient analysis with fast Wilson-Daubechies time-frequency transform"
7420:
7403:
7248:
6760:
Wavelet Analysis and Applications (See: Unitary systems and wavelet sets)
6625:
6605:
6543:
5432:
5400:
5018:
4915:
4812:
wavelets, separate decomposition and reconstruction filters are defined.
4124:{\textstyle \operatorname {rect} \left({\frac {t-u}{\Delta _{t}}}\right)}
178:
99:
68:
63:
35:
20:
5071:
A wavelet is a mathematical function used to divide a given function or
4902:
Notable contributions to wavelet theory since then can be attributed to
3305:{\displaystyle \int _{-\infty }^{\infty }|\psi (t)|^{2}\,dt<\infty .}
1346:
534:
9470:
8950:
8650:
8581:
8531:
8506:
8426:
7975:
7627:
6858:
Mallat, Stephane. "A wavelet tour of signal processing. 1998." 250-252.
5364:
5356:
5044:
5028:
4969:
9/7 wavelet transform (developed by Ingrid Daubechies in 1992) for its
4931:
4896:
4745:
3895:, in which signals are represented as a sum of sinusoids. In fact, the
3886:
965:
301:
279:
142:
7678:
7551:
7072:
6942:"Zweig, George -- from Eric Weisstein's World of Scientific Biography"
6680:
6392:(Sometimes referred to as CDF N/P or Daubechies biorthogonal wavelets)
1342:
Multiresolution based discrete wavelet transforms (continuous in time)
9623:
9475:
9095:
8890:
8802:
8787:
8782:
8747:
8378:"How Wavelets Allow Researchers to Transform â and Understand â Data"
8206:"How Wavelets Allow Researchers to Transform â and Understand â Data"
6794:
6574:
6222:
is called the shrinkage factor, which depends on the prior variances
5340:
5292:
5288:
5253:
5226:
5054:
4978:
4950:
4822:
Daubechies and Symlet wavelets can be defined by the scaling filter.
4780:). (For instance, a logarithmic Fourier Transform also exists with O(
4706:
3958:
312:
Continuous wavelet transforms (continuous shift and scale parameters)
134:
39:
7980:
Multiresolution Signal Decomposition: Transforms, Subbands, Wavelets
6868:
5443:
355:. For the example of the scale one frequency band this function is
198:
9139:
8757:
8634:
8629:
8624:
8264:
external links, and converting useful links where appropriate into
7589:
6615:
6595:
6528:
5295:
standard. Wavelet OFDM can achieve deeper notches than traditional
3474:
3225:{\displaystyle \int _{-\infty }^{\infty }|\psi (t)|\,dt<\infty }
3083:
552:
or frequency band is generated by the functions (sometimes called
498:
321:
59:
8315:
7727:"Wavelet-based multiscale similarity measure for complex networks"
50:
10644:
7401:
6383:
5396:
5331:. Many areas of physics have seen this paradigm shift, including
5202:
4946:(SPIHT) developed by Amir Said with William A. Pearlman in 1996.
3073:
also involving a memory-efficient time-recursive implementation.
1969:
are the orthogonal "differences" of the above sequence, that is,
1394:
From the mother and father wavelets one constructs the subspaces
8170:
4792:
A wavelet (or a wavelet family) can be defined in various ways:
3566:{\displaystyle \int _{-\infty }^{\infty }t^{m}\,\psi (t)\,dt=0.}
2476:{\displaystyle h_{n}=\langle \psi _{0,0},\,\phi _{-1,n}\rangle }
2310:{\displaystyle g_{n}=\langle \phi _{0,0},\,\phi _{-1,n}\rangle }
491:. That, Meyer's, and two other examples of mother wavelets are:
10566:
9547:
9521:
9501:
8752:
8543:
6582:
for computing periodicity in any including unevenly spaced data
6427:
5913:
is sparse, one method is to apply a Gaussian mixture model for
5360:
5280:
1387:= 1. The most famous pair of father and mother wavelets is the
58:
For example, a wavelet could be created to have a frequency of
7061:
IEEE Transactions on Circuits and Systems for Video Technology
3444:{\displaystyle \int _{-\infty }^{\infty }|\psi (t)|^{2}\,dt=1}
2078:
From those inclusions and orthogonality relations, especially
8395:
7847:
7724:
6971:
4842:
all the spectrum is covered. See for a detailed explanation.
2991:{\displaystyle c_{j_{0},k}=\langle S,\phi _{j_{0},k}\rangle }
118:
of square-integrable functions. This is accomplished through
7790:
7784:
6725:
Daubechies, Ingrid. (1992), Ten Lectures on Wavelets, SIAM,
6347:
at different timescales. Climate networks constructed using
5860:{\displaystyle z\ \sim \ \ {\mathcal {N}}(0,\,\sigma ^{2}I)}
5543:
has a sparse representation in a certain wavelet basis, and
5193:
electron optical transforms intermediate between direct and
3143:{\displaystyle L^{1}(\mathbb {R} )\cap L^{2}(\mathbb {R} ).}
1743:
keeps the time domain properties, while the mother wavelets
1138:
A sufficient condition for the reconstruction of any signal
8486:
7917:
http://matlab.izmiran.ru/help/toolbox/wavelet/ch06_a32.html
7718:
5276:
4958:
31:
6762:, Appl. Numer. Harmon. Anal., BirkhĂ€user, pp. 143â171
5598:{\displaystyle v\ \sim \ {\mathcal {N}}(0,\,\sigma ^{2}I)}
4875:
can be defined by a wavelet function. See a list of a few
7127:"Mathematical properties of the JPEG2000 wavelet filters"
5392:
4632:{\displaystyle \operatorname {sinc} (\Delta _{t}\omega )}
3575:
The mother wavelet is scaled (or dilated) by a factor of
157:), can result in a complex pattern of varying intensity.
7964:, Society for Industrial and Applied Mathematics, 1992,
7493:
4639:
function in the frequency domain, resulting in spurious
3367:{\displaystyle \int _{-\infty }^{\infty }\psi (t)\,dt=0}
7933:
http://www.ansatt.hig.no/erikh/papers/scia99/node6.html
7841:
6289:
At last, apply the inverse wavelet transform to obtain
4744:
The discrete wavelet transform is less computationally
271:. Discrete wavelet transform (continuous in time) of a
71:
is at the core of many practical wavelet applications.
8179:(3rd ed.), New York: Cambridge University Press,
4081:
3058:{\displaystyle d_{j,k}=\langle S,\psi _{j,k}\rangle .}
2489:
2323:
7193:
Understanding Digital Cinema: A Professional Handbook
6295:
6260:
6228:
6199:
6129:
6094:
6062:
5942:
5919:
5899:
5875:
5808:
5788:
5749:
5743:
is the wavelet transform of the signal component and
5713:
5633:
5613:
5549:
5529:
5509:
5489:
5457:
4682:
4649:
4603:
4465:
4446:
4334:
4172:
4137:
4046:
3974:
3905:
3859:
3717:
3591:
3508:
3484:). Most constructions of discrete WT make use of the
3380:
3320:
3238:
3168:
3091:
3004:
2926:
2779:
2746:
2595:
2414:
2248:
2194:
2140:
2084:
1999:
1907:
1779:
1749:
1722:
1559:
1400:
1273:
1148:
1026:
815:
689:
562:
361:
10308:
Autoregressive conditional heteroskedasticity (ARCH)
5291:), and in one of the optional modes included in the
4930:'s non-orthogonal multiresolution framework (1989),
3887:
Comparisons with Fourier transform (continuous-time)
653:
is any real number and defines the shift. The pair (
8103:Ramazan Gençay, Faruk Selçuk and Brandon Whitcher,
4926:' orthogonal wavelets with compact support (1988),
4856:Meyer wavelets can be defined by scaling functions
4838:) (also called father wavelet) in the time domain.
4834:) (i.e. the mother wavelet) and scaling function Ï(
1319:{\displaystyle \{\psi _{m,n}:m,n\in \mathbb {Z} \}}
964:, one can assemble the wavelet coefficients into a
9770:
8332:Course on Wavelets given at UC Santa Barbara, 2004
8177:Numerical Recipes: The Art of Scientific Computing
6923:"A Really Friendly Guide To Wavelets â PolyValens"
6328:
6278:
6246:
6214:
6185:
6112:
6088:is the variance of "significant" coefficients and
6080:
6048:
5925:
5905:
5881:
5859:
5794:
5771:
5735:
5699:
5619:
5597:
5535:
5515:
5495:
5475:
5447:Signal denoising by wavelet transform thresholding
5302:
5182:Another example of a generalized transform is the
4697:
4668:
4631:
4587:
4452:
4430:
4316:
4150:
4123:
4067:
4032:
3945:
3874:
3817:
3668:
3565:
3443:
3366:
3304:
3224:
3142:
3057:
2990:
2912:
2765:
2732:
2566:
2475:
2400:
2309:
2234:
2180:
2126:
2047:
1961:
1885:
1762:
1735:
1708:
1546:
1318:
1259:
1128:
950:
798:
637:
479:
8248:may not follow Knowledge's policies or guidelines
7291:(M.S. Thesis in Physics, U. Missouri â St. Louis)
7260:
6120:is the variance of "insignificant" coefficients.
5779:is the wavelet transform of the noise component.
4891:'s work in the early 20th century. Later work by
3891:The wavelet transform is often compared with the
129:, the diffraction phenomenon is described by the
10723:
8028:Adapted Wavelet Analysis From Theory to Software
7628:V Necula, S Klimenko and G Mitselmakher (2012).
7093:
6772:
5245:if a signal is already sampled, and the CWT for
1962:{\displaystyle \dots ,W_{1},W_{0},W_{-1},\dots }
9856:Multivariate adaptive regression splines (MARS)
7446:
5241:Generally, an approximation to DWT is used for
4830:Wavelets are defined by the wavelet function Ï(
3583:to give (under Morlet's original formulation):
2235:{\displaystyle g=\{g_{n}\}_{n\in \mathbb {Z} }}
2181:{\displaystyle h=\{h_{n}\}_{n\in \mathbb {Z} }}
7948:Zur Theorie der orthogonalen Funktionensysteme
7529:
7378:A.N. Akansu, W.A. Serdijn and I.W. Selesnick,
4953:standard was developed from 1997 to 2000 by a
8411:
7027:
6338:
6186:{\displaystyle {\tilde {p}}=E(p/y)=\tau (y)y}
7224:(Butterworths, London/Krieger, Malabar FLA)
7058:
3469:, one needs at least the condition that the
3049:
3024:
2985:
2953:
2470:
2428:
2304:
2262:
2215:
2201:
2161:
2147:
1786:
1780:
1773:From these it is required that the sequence
1313:
1274:
1226:
1200:
881:
856:
835:
829:
743:
737:
16:Function for integral Fourier-like transform
7380:Emerging applications of wavelets: A review
7343:
7303:Applied and Computational Harmonic Analysis
7094:Taubman, David; Marcellin, Michael (2012).
6879:
4033:{\displaystyle \psi (t)=g(t-u)e^{-2\pi it}}
3579:and translated (or shifted) by a factor of
3495:of vanishing moments, i.e. for all integer
3473:is a representation of the identity in the
2574:The second identity of the first pair is a
227:. Unsourced material may be challenged and
8456:
8418:
8404:
8120:The Illustrated Wavelet Transform Handbook
7332:Digital implementation of ridgelet packets
6398:(2, 4, 6, 8, 10, 12, 14, 16, 18, 20, etc.)
6379:Biorthogonal nearly coiflet (BNC) wavelets
6329:{\displaystyle {\tilde {s}}=W{\tilde {p}}}
5700:{\displaystyle y=W^{T}x=W^{T}s+W^{T}v=p+z}
5403:, human sexual response analysis, general
4787:
2048:{\displaystyle V_{m}\oplus W_{m}=V_{m-1}.}
86:In formal terms, this representation is a
9069:
8284:Learn how and when to remove this message
8088:Donald B. Percival and Andrew T. Walden,
7889:
7816:
7689:
7653:
7588:
7419:
6898:
6835:
6825:
6807:
6027:
5974:
5840:
5578:
5201:of atom clustering, i.e. in the study of
5170:
4734:four separate Fourier transforms required
4578:
4421:
4307:
4226:
4166:, one may define the wavelet's energy as
3808:
3550:
3537:
3428:
3351:
3286:
3209:
3130:
3106:
2524:
2450:
2358:
2284:
2226:
2172:
1876:
1608:
1449:
1309:
1209:
1194:
1176:
938:
893:
789:
718:
661:) defines a point in the right halfplane
402:
380:
247:Learn how and when to remove this message
8090:Wavelet Methods for Time Series Analysis
7692:Mechanical Systems and Signal Processing
7124:
6964:
6404:(Also referred to as Daubechies wavelet)
5442:
4727:
4705:. The window function may be some other
2127:{\displaystyle V_{0}\oplus W_{0}=V_{-1}}
1359:. This means that there has to exist an
1345:
533:
515:
497:
133:that treats each point in a propagating
49:
8349:The Fractional Spline Wavelet Transform
7000:The Essential Guide to Video Processing
6880:Haines, VG. V.; Jones, Alan G. (1988).
5279:is the basic modulation scheme used in
5099:Wavelet transforms are classified into
3067:
1770:keeps the frequency domain properties.
267:(analog) signals and so are related to
10724:
10382:KaplanâMeier estimator (product limit)
7572:
7520:An overview of P1901 PHY/MAC proposal.
7189:
6757:
6658:
6433:
5114:but the common ones are listed below:
4944:set partitioning in hierarchical trees
4845:For a wavelet with compact support, Ï(
4669:{\displaystyle \Delta _{t}\to \infty }
3451:is the condition for square norm one.
649:is positive and defines the scale and
291:(IIR) filters. The wavelets forming a
10455:
10022:
9769:
9068:
8838:
8455:
8399:
8339:(Introductory (for very smart kids!))
7634:Journal of Physics: Conference Series
7487:
7300:F. G. Meyer and R. R. Coifman (1997)
7134:IEEE Transactions on Image Processing
7118:
7102:Springer Science & Business Media
6996:
6965:Sullivan, Gary (8â12 December 2003).
6939:
5060:
4720:In contrast, the wavelet transform's
3946:{\displaystyle \psi (t)=e^{-2\pi it}}
2134:, follows the existence of sequences
10692:
10392:Accelerated failure time (AFT) model
8228:
8092:, Cambridge University Press, 2000,
7222:Electron microscopy of thin crystals
7052:
6360:
5438:
5031:, Didier Le Gall, Ali J. Tabatabai,
3374:is the condition for zero mean, and
225:adding citations to reliable sources
192:
10704:
9987:Analysis of variance (ANOVA, anova)
8839:
8371:A Really Friendly Guide To Wavelets
8173:"Section 13.10. Wavelet Transforms"
7453:Construction and Building Materials
6355:
5371:. This change has also occurred in
4859:
4825:
1379:is an integer. A typical choice is
13:
10082:CochranâMantelâHaenszel statistics
8708:Pearson product-moment correlation
8159:, Society of Applied Mathematics,
7998:Multirate Systems and Filter Banks
7940:
6900:10.1111/j.1365-246X.1988.tb01131.x
6564:Gabor wavelet § Wavelet space
6013:
5960:
5826:
5564:
5451:Suppose we measure a noisy signal
5112:list of wavelet-related transforms
4717:determined by the sampling width.
4663:
4651:
4614:
4264:
4259:
4192:
4187:
4139:
4106:
3860:
3743:
3738:
3686:) varies over the full half-plane
3522:
3517:
3394:
3389:
3334:
3329:
3296:
3252:
3247:
3219:
3182:
3177:
145:. This is due to the addition, or
14:
10753:
8224:
7797:Nonlinear Processes in Geophysics
7465:10.1016/j.conbuildmat.2023.133453
6869:http://www.dspguide.com/ch8/4.htm
6808:Lindeberg, T. (23 January 2023).
6485:
6390:Cohen-Daubechies-Feauveau wavelet
5211:transmission electron microscopes
4795:
3678:For the continuous WT, the pair (
3082:functions from a subspace of the
3076:
188:
177:meaning "small wave" was used by
10703:
10691:
10679:
10666:
10665:
10456:
8365:Concise Introduction to Wavelets
8321:Binomial-QMF Daubechies Wavelets
8233:
5411:, acoustics, vibration signals,
4955:Joint Photographic Experts Group
2061:one may conclude that the space
1976:is the orthogonal complement of
1142:of finite energy by the formula
988:system for some real parameters
197:
19:For the concept in physics, see
10341:Least-squares spectral analysis
7921:
7906:
7734:The European Physical Journal B
7683:
7671:
7662:
7621:
7566:
7523:
7440:
7395:
7385:
7372:
7337:
7312:
7294:
7281:
7254:
7234:
7214:
7183:
7087:
7021:
6990:
6958:
6933:
6915:
6882:"Logarithmic Fourier Transform"
6873:
6861:
6852:
6580:Least-squares spectral analysis
6279:{\displaystyle \sigma _{2}^{2}}
6247:{\displaystyle \sigma _{1}^{2}}
6113:{\displaystyle \sigma _{2}^{2}}
6081:{\displaystyle \sigma _{1}^{2}}
5303:As a representation of a signal
5236:
4985:extension, was selected as the
4981:technology, which includes the
4961:format, JPEG 2000 instead uses
960:For the analysis of the signal
9322:Mean-unbiased minimum-variance
8425:
8355:based on fractional b-Splines.
7655:10.1088/1742-6596/363/1/012032
6801:
6766:
6751:
6735:
6719:
6703:
6687:
6652:
6643:
6438:
6320:
6302:
6209:
6203:
6177:
6171:
6162:
6148:
6136:
6043:
6018:
6008:
5996:
5990:
5965:
5854:
5831:
5592:
5569:
4965:(DWT) algorithms. It uses the
4692:
4686:
4660:
4626:
4610:
4568:
4563:
4557:
4551:
4541:
4530:
4515:
4473:
4411:
4406:
4400:
4393:
4382:
4367:
4297:
4292:
4286:
4280:
4270:
4216:
4211:
4205:
4198:
4062:
4050:
4005:
3993:
3984:
3978:
3915:
3909:
3869:
3863:
3776:
3770:
3614:
3608:
3547:
3541:
3418:
3413:
3407:
3400:
3348:
3342:
3276:
3271:
3265:
3258:
3205:
3201:
3195:
3188:
3134:
3126:
3110:
3102:
2558:
2543:
2499:
2493:
2392:
2377:
2333:
2327:
1880:
1872:
1700:
1675:
1645:
1639:
1612:
1579:
1541:
1516:
1486:
1480:
1453:
1420:
1254:
1248:
1158:
1152:
1049:
1043:
934:
928:
908:
902:
850:
838:
786:
780:
758:
746:
706:
700:
585:
579:
463:
454:
442:
430:
415:
409:
396:
387:
371:
365:
1:
10635:Geographic information system
9851:Simultaneous equations models
7275:10.1016/s0304-3991(98)00035-7
6637:
5607:Let the wavelet transform of
5523:represents the noise. Assume
5197:have been widely used in the
5105:continuous wavelet transforms
675:The projection of a function
318:continuous wavelet transforms
261:time-frequency representation
9818:Coefficient of determination
9429:Uniformly most powerful test
8353:fractional wavelet transform
8337:Wavelets for Kids (PDF file)
8026:Mladen Victor Wickerhauser,
8013:A Friendly Guide to Wavelets
7496:IEEE Communications Magazine
7242:Microscopy and Microanalysis
6621:Short-time Fourier transform
6559:Fractional Fourier transform
5318:short-time Fourier transform
5164:Fractional wavelet transform
5158:Fractional Fourier transform
5152:Stationary wavelet transform
5146:Wavelet packet decomposition
5119:Continuous wavelet transform
4908:continuous wavelet transform
3963:short-time Fourier transform
3460:continuous wavelet transform
2242:that satisfy the identities
293:continuous wavelet transform
160:
7:
10387:Proportional hazards models
10331:Spectral density estimation
10313:Vector autoregression (VAR)
9747:Maximum posterior estimator
8979:Randomized controlled trial
8343:WITS: Where Is The Starlet?
8304:Encyclopedia of Mathematics
7927:Erik HjelmÄs (1999-01-21)
7712:10.1016/j.ymssp.2009.02.008
7334:(Academic Press, New York).
7190:Swartz, Charles S. (2005).
7125:Unser, M.; Blu, T. (2003).
6517:
6492:Complex Mexican hat wavelet
6345:Climate as complex networks
5217:of all sorts, the range of
5101:discrete wavelet transforms
4996:
4151:{\displaystyle \Delta _{t}}
2920:where the coefficients are
2740:For any signal or function
679:onto the subspace of scale
10:
10758:
10147:Multivariate distributions
8567:Average absolute deviation
7874:10.1038/s41598-019-45423-5
7754:10.1140/epjb/e2018-90460-6
7607:10.1103/PhysRevD.93.122004
7392:10.1007/s10346-015-0589-y.
7038:10.1109/ICASSP.1988.196696
7032:. pp. 761â764 vol.2.
6977:Video Coding Experts Group
6827:10.1007/s00422-022-00953-6
6633:radio â transmits wavelets
6549:Fourier-related transforms
6339:Multiscale climate network
5503:represents the signal and
5141:generalized lifting scheme
5125:Discrete wavelet transform
5064:
4963:discrete wavelet transform
4940:harmonic wavelet transform
4882:
3882:has a finite time interval
3467:discrete wavelet transform
2766:{\displaystyle S\in L^{2}}
2075:roughly covers the band .
275:(sampled) signal by using
92:square-integrable function
18:
10661:
10615:
10552:
10505:
10468:
10464:
10451:
10423:
10405:
10372:
10363:
10321:
10268:
10229:
10178:
10169:
10135:Structural equation model
10090:
10047:
10043:
10018:
9977:
9943:
9897:
9864:
9826:
9793:
9789:
9765:
9705:
9614:
9533:
9497:
9488:
9471:Score/Lagrange multiplier
9456:
9409:
9354:
9280:
9271:
9081:
9077:
9064:
9023:
8997:
8949:
8904:
8886:Sample size determination
8851:
8847:
8834:
8738:
8693:
8667:
8649:
8605:
8557:
8477:
8468:
8464:
8451:
8433:
7954:, pp. 331â371, 1910.
7950:, Mathematische Annalen,
7508:10.1109/MCOM.2008.4557044
7358:10.1007/s11432-011-4320-x
6758:Larson, David R. (2007),
6569:HuygensâFresnel principle
5802:are 0 or close to 0, and
5351:transient data analysis,
5285:power line communications
295:(CWT) are subject to the
289:infinite impulse response
131:HuygensâFresnel principle
94:with respect to either a
81:wavelet-based compression
10630:Environmental statistics
10152:Elliptical distributions
9945:Generalized linear model
9874:Simple linear regression
9644:HodgesâLehmann estimator
9101:Probability distribution
9010:Stochastic approximation
8572:Coefficient of variation
8107:, Academic Press, 2001,
8030:, A K Peters Ltd, 1994,
7982:, Academic Press, 1992,
7962:Ten Lectures on Wavelets
6946:scienceworld.wolfram.com
6591:Multiresolution analysis
6215:{\displaystyle \tau (y)}
5772:{\displaystyle z=W^{T}v}
5736:{\displaystyle p=W^{T}s}
5322:multiresolution analysis
5287:technology developed by
5262:frames of a vector space
4817:quadrature mirror filter
4804:(FIR) filter of length 2
4075:can often be written as
3875:{\displaystyle \Psi (t)}
3486:multiresolution analysis
3458:to be a wavelet for the
3154:functions that are both
1895:multiresolution analysis
1357:multiresolution analysis
1355:shifted wavelets form a
10737:Timeâfrequency analysis
10290:Cross-correlation (XCF)
9898:Non-standard predictors
9332:LehmannâScheffĂ© theorem
9005:Adaptive clinical trial
8000:, Prentice Hall, 1993,
7818:10.5194/npg-24-599-2017
7154:10.1109/TIP.2003.812329
6997:Bovik, Alan C. (2009).
6512:Modified Morlet wavelet
4802:finite impulse response
4788:Definition of a wavelet
1901:and that the subspaces
285:finite impulse response
151:closely spaced openings
112:frame of a vector space
10686:Mathematics portal
10507:Engineering statistics
10415:NelsonâAalen estimator
9992:Analysis of covariance
9879:Ordinary least squares
9803:Pearson product-moment
9207:Statistical functional
9118:Empirical distribution
8951:Controlled experiments
8680:Frequency distribution
8458:Descriptive statistics
8153:Jackie (Jianhong) Shen
7249:arXiv:cond-mat/0403017
6814:Biological Cybernetics
6330:
6280:
6248:
6216:
6187:
6114:
6082:
6050:
5927:
5907:
5883:
5861:
5796:
5773:
5737:
5701:
5621:
5599:
5537:
5517:
5497:
5477:
5448:
5171:Generalized transforms
5131:Fast wavelet transform
5073:continuous-time signal
4766:fast Fourier transform
4756:time as compared to O(
4741:
4699:
4670:
4633:
4589:
4454:
4432:
4318:
4152:
4125:
4069:
4068:{\displaystyle g(t-u)}
4034:
3947:
3876:
3819:
3670:
3567:
3445:
3368:
3306:
3226:
3144:
3059:
2992:
2914:
2767:
2734:
2580:fast wavelet transform
2568:
2477:
2402:
2311:
2236:
2182:
2128:
2049:
1963:
1887:
1764:
1737:
1710:
1548:
1351:
1320:
1267:is that the functions
1261:
1130:
952:
800:
639:
548:The subspace of scale
541:
523:
505:
487:with the (normalized)
481:
55:
10602:Population statistics
10544:System identification
10278:Autocorrelation (ACF)
10206:Exponential smoothing
10120:Discriminant analysis
10115:Canonical correlation
9979:Partition of variance
9841:Regression validation
9685:(JonckheereâTerpstra)
9584:Likelihood-ratio test
9273:Frequentist inference
9185:Locationâscale family
9106:Sampling distribution
9071:Statistical inference
9038:Cross-sectional study
9025:Observational studies
8984:Randomized experiment
8813:Stem-and-leaf display
8615:Central limit theorem
8053:Barbara Burke Hubbard
6601:Non-separable wavelet
6331:
6281:
6249:
6217:
6188:
6115:
6083:
6051:
5928:
5908:
5884:
5862:
5797:
5774:
5738:
5702:
5622:
5600:
5538:
5518:
5498:
5478:
5476:{\displaystyle x=s+v}
5446:
5417:multifractal analysis
4987:video coding standard
4731:
4700:
4671:
4634:
4590:
4455:
4433:
4319:
4153:
4126:
4070:
4035:
3957:is only localized in
3948:
3877:
3820:
3671:
3568:
3446:
3369:
3307:
3227:
3156:absolutely integrable
3150:This is the space of
3145:
3060:
2993:
2915:
2768:
2735:
2569:
2478:
2403:
2312:
2237:
2183:
2129:
2050:
1964:
1888:
1765:
1763:{\displaystyle W_{i}}
1738:
1736:{\displaystyle V_{i}}
1711:
1549:
1349:
1321:
1262:
1131:
953:
801:
640:
537:
519:
501:
482:
297:uncertainty principle
53:
10525:Probabilistic design
10110:Principal components
9953:Exponential families
9905:Nonlinear regression
9884:General linear model
9846:Mixed effects models
9836:Errors and residuals
9813:Confounding variable
9715:Bayesian probability
9693:Van der Waerden test
9683:Ordered alternative
9448:Multiple comparisons
9327:RaoâBlackwellization
9290:Estimating equations
9246:Statistical distance
8964:Factorial experiment
8497:Arithmetic-Geometric
8254:improve this article
8124:Institute of Physics
8015:, Birkhauser, 1994,
7978:and Richard Haddad,
7421:10.3390/math11224644
7326:, R. R. Coifman and
7247::S2, 1010â1011 (cf.
7198:Taylor & Francis
6293:
6258:
6226:
6197:
6127:
6092:
6060:
5940:
5917:
5897:
5873:
5806:
5786:
5747:
5711:
5631:
5611:
5547:
5527:
5507:
5487:
5455:
4975:lossless compression
4906:âs discovery of the
4873:Mexican hat wavelets
4740:transform basis set.
4698:{\displaystyle x(t)}
4680:
4647:
4601:
4463:
4453:{\displaystyle \xi }
4444:
4332:
4170:
4135:
4079:
4044:
3972:
3903:
3857:
3715:
3589:
3506:
3378:
3318:
3236:
3166:
3089:
3068:Time-causal wavelets
3002:
2924:
2777:
2744:
2593:
2487:
2412:
2321:
2246:
2192:
2138:
2082:
1997:
1983:inside the subspace
1905:
1777:
1747:
1720:
1557:
1398:
1271:
1146:
1024:
1016:. The corresponding
813:
808:wavelet coefficients
687:
560:
359:
221:improve this section
185:in the early 1980s.
90:representation of a
10597:Official statistics
10520:Methods engineering
10201:Seasonal adjustment
9969:Poisson regressions
9889:Bayesian regression
9828:Regression analysis
9808:Partial correlation
9780:Regression analysis
9379:Prediction interval
9374:Likelihood interval
9364:Confidence interval
9356:Interval estimation
9317:Unbiased estimators
9135:Model specification
9015:Up-and-down designs
8703:Partial correlation
8659:Index of dispersion
8577:Interquartile range
8266:footnote references
7866:2019NatSR...9.8808A
7809:2017NPGeo..24..599A
7746:2018EPJB...91..296A
7704:2009MSSP...23.1554R
7646:2012JPhCS.363a2032N
7599:2016PhRvD..93l2004A
7544:2009JPCA..113...19W
7346:Sci. China Inf. Sci
7287:Martin Rose (2006)
7146:2003ITIP...12.1080U
6940:Weisstein, Eric W.
6890:Geophysical Journal
6787:1992OptEn..31.1825S
6775:Optical Engineering
6673:1953Geop...18..769R
6571:(physical wavelets)
6554:Fractal compression
6539:Dimension reduction
6460:Mexican hat wavelet
6434:Continuous wavelets
6386:(6, 12, 18, 24, 30)
6275:
6243:
6109:
6077:
6042:
5989:
5266:wavelet compression
5219:pattern recognition
5049:Victor Wickerhauser
4877:continuous wavelets
4489:
4349:
4268:
4196:
3747:
3526:
3398:
3338:
3256:
3186:
3152:Lebesgue measurable
2576:refinement equation
1716:The father wavelet
973:Continuous wavelets
971:See a list of some
155:diffraction grating
10617:Spatial statistics
10497:Medical statistics
10397:First hitting time
10351:Whittle likelihood
10002:Degrees of freedom
9997:Multivariate ANOVA
9930:Heteroscedasticity
9742:Bayesian estimator
9707:Bayesian inference
9556:KolmogorovâSmirnov
9441:Randomization test
9411:Testing hypotheses
9384:Tolerance interval
9295:Maximum likelihood
9190:Exponential family
9123:Density estimation
9083:Statistical theory
9043:Natural experiment
8989:Scientific control
8906:Survey methodology
8592:Standard deviation
8367:by René Puschinger
8299:"Wavelet analysis"
7994:P. P. Vaidyanathan
7854:Scientific Reports
6927:www.polyvalens.com
6611:Scaled correlation
6524:Chirplet transform
6423:Villasenor wavelet
6396:Daubechies wavelet
6326:
6276:
6261:
6244:
6229:
6212:
6183:
6110:
6095:
6078:
6063:
6046:
6028:
5975:
5923:
5903:
5879:
5857:
5792:
5769:
5733:
5697:
5617:
5595:
5533:
5513:
5493:
5473:
5449:
5409:speech recognition
5349:gravitational wave
5333:molecular dynamics
5314:compressed sensing
5184:chirplet transform
5086:Fourier transforms
5061:Wavelet transforms
4742:
4695:
4666:
4629:
4585:
4466:
4450:
4428:
4335:
4314:
4251:
4179:
4164:Parseval's theorem
4148:
4121:
4065:
4030:
3943:
3872:
3815:
3730:
3666:
3563:
3509:
3441:
3381:
3364:
3321:
3302:
3239:
3222:
3169:
3162:in the sense that
3140:
3055:
2988:
2910:
2877:
2867:
2795:
2763:
2730:
2564:
2529:
2473:
2398:
2363:
2307:
2232:
2178:
2124:
2057:In analogy to the
2045:
1959:
1883:
1760:
1733:
1706:
1544:
1361:auxiliary function
1352:
1316:
1257:
1199:
1181:
1126:
948:
796:
683:then has the form
635:
542:
524:
506:
477:
56:
10742:Signal processing
10719:
10718:
10657:
10656:
10653:
10652:
10592:National accounts
10562:Actuarial science
10554:Social statistics
10447:
10446:
10443:
10442:
10439:
10438:
10374:Survival function
10359:
10358:
10221:Granger causality
10062:Contingency table
10037:Survival analysis
10014:
10013:
10010:
10009:
9866:Linear regression
9761:
9760:
9757:
9756:
9732:Credible interval
9701:
9700:
9484:
9483:
9300:Method of moments
9169:Parametric family
9130:Statistical model
9060:
9059:
9056:
9055:
8974:Random assignment
8896:Statistical power
8830:
8829:
8826:
8825:
8675:Contingency table
8645:
8644:
8512:Generalized/power
8373:by Clemens Valens
8294:
8293:
8286:
8186:978-0-521-88068-8
8118:Paul S. Addison,
8069:978-1-56881-072-0
7958:Ingrid Daubechies
7552:10.1021/jp804420g
7073:10.1109/76.499834
6747:978-0-12-047141-6
6731:978-0-89871-274-2
6681:10.1190/1.1437927
6480:Strömberg wavelet
6450:Hermitian wavelet
6361:Discrete wavelets
6323:
6305:
6139:
5954:
5948:
5926:{\displaystyle p}
5906:{\displaystyle p}
5882:{\displaystyle W}
5823:
5820:
5814:
5795:{\displaystyle p}
5782:Most elements in
5620:{\displaystyle x}
5561:
5555:
5536:{\displaystyle s}
5516:{\displaystyle v}
5496:{\displaystyle s}
5439:Wavelet denoising
5413:computer graphics
5405:signal processing
5369:quantum mechanics
5329:Fourier transform
5316:. (Note that the
5199:harmonic analysis
5067:Wavelet transform
5037:Ingrid Daubechies
5027:Since the 1980s:
5013:Since the 1970s:
4971:lossy compression
4924:Ingrid Daubechies
4920:discrete wavelets
4722:multiresolutional
4641:ringing artifacts
4554:
4509:
4476:
4361:
4283:
4249:
4115:
3955:Fourier transform
3897:Fourier transform
3893:Fourier transform
3802:
3728:
3727:
3657:
3632:
3630:
3160:square integrable
2868:
2845:
2786:
2512:
2510:
2346:
2344:
1621:
1620: where
1462:
1461: where
1328:orthonormal basis
1182:
1164:
1117:
1072:
1071:
1020:are now given as
626:
601:
600:
546:
545:
528:
527:
510:
509:
475:
269:harmonic analysis
257:
256:
249:
127:classical physics
45:signal processing
10749:
10707:
10706:
10695:
10694:
10684:
10683:
10669:
10668:
10572:Crime statistics
10466:
10465:
10453:
10452:
10370:
10369:
10336:Fourier analysis
10323:Frequency domain
10303:
10250:
10216:Structural break
10176:
10175:
10125:Cluster analysis
10072:Log-linear model
10045:
10044:
10020:
10019:
9961:
9935:Homoscedasticity
9791:
9790:
9767:
9766:
9686:
9678:
9670:
9669:(KruskalâWallis)
9654:
9639:
9594:Cross validation
9579:
9561:AndersonâDarling
9508:
9495:
9494:
9466:Likelihood-ratio
9458:Parametric tests
9436:Permutation test
9419:1- & 2-tails
9310:Minimum distance
9282:Point estimation
9278:
9277:
9229:Optimal decision
9180:
9079:
9078:
9066:
9065:
9048:Quasi-experiment
8998:Adaptive designs
8849:
8848:
8836:
8835:
8713:Rank correlation
8475:
8474:
8466:
8465:
8453:
8452:
8420:
8413:
8406:
8397:
8396:
8392:
8390:
8389:
8312:
8289:
8282:
8278:
8275:
8269:
8237:
8236:
8229:
8220:
8218:
8217:
8200:
8199:
8198:
8189:, archived from
7935:
7925:
7919:
7910:
7904:
7903:
7893:
7845:
7839:
7838:
7820:
7788:
7782:
7781:
7731:
7722:
7716:
7715:
7687:
7681:
7675:
7669:
7666:
7660:
7659:
7657:
7625:
7619:
7618:
7592:
7570:
7564:
7563:
7527:
7521:
7519:
7491:
7485:
7484:
7444:
7438:
7437:
7423:
7399:
7393:
7389:
7383:
7376:
7370:
7369:
7352:(6): 1270â1279.
7341:
7335:
7316:
7310:
7298:
7292:
7285:
7279:
7278:
7258:
7252:
7238:
7232:
7218:
7212:
7211:
7187:
7181:
7180:
7178:
7172:. Archived from
7140:(9): 1080â1090.
7131:
7122:
7116:
7115:
7091:
7085:
7084:
7056:
7050:
7049:
7025:
7019:
7018:
6994:
6988:
6987:
6985:
6983:
6962:
6956:
6955:
6953:
6952:
6937:
6931:
6930:
6919:
6913:
6912:
6902:
6886:
6877:
6871:
6865:
6859:
6856:
6850:
6849:
6839:
6829:
6805:
6799:
6798:
6795:10.1117/12.59911
6770:
6764:
6763:
6755:
6749:
6739:
6733:
6723:
6717:
6707:
6701:
6691:
6685:
6684:
6656:
6650:
6647:
6418:Legendre wavelet
6356:List of wavelets
6335:
6333:
6332:
6327:
6325:
6324:
6316:
6307:
6306:
6298:
6285:
6283:
6282:
6277:
6274:
6269:
6253:
6251:
6250:
6245:
6242:
6237:
6221:
6219:
6218:
6213:
6192:
6190:
6189:
6184:
6158:
6141:
6140:
6132:
6119:
6117:
6116:
6111:
6108:
6103:
6087:
6085:
6084:
6079:
6076:
6071:
6055:
6053:
6052:
6047:
6041:
6036:
6017:
6016:
5988:
5983:
5964:
5963:
5952:
5946:
5932:
5930:
5929:
5924:
5912:
5910:
5909:
5904:
5888:
5886:
5885:
5880:
5866:
5864:
5863:
5858:
5850:
5849:
5830:
5829:
5821:
5818:
5812:
5801:
5799:
5798:
5793:
5778:
5776:
5775:
5770:
5765:
5764:
5742:
5740:
5739:
5734:
5729:
5728:
5706:
5704:
5703:
5698:
5681:
5680:
5665:
5664:
5649:
5648:
5626:
5624:
5623:
5618:
5604:
5602:
5601:
5596:
5588:
5587:
5568:
5567:
5559:
5553:
5542:
5540:
5539:
5534:
5522:
5520:
5519:
5514:
5502:
5500:
5499:
5494:
5482:
5480:
5479:
5474:
5431:, the notion of
5429:image processing
5373:image processing
5310:Gibbs phenomenon
5243:data compression
5195:reciprocal space
5177:Heisenberg group
4983:Motion JPEG 2000
4860:Wavelet function
4826:Scaling function
4776:would require O(
4707:apodizing filter
4704:
4702:
4701:
4696:
4675:
4673:
4672:
4667:
4659:
4658:
4638:
4636:
4635:
4630:
4622:
4621:
4594:
4592:
4591:
4586:
4577:
4576:
4571:
4556:
4555:
4547:
4544:
4539:
4538:
4533:
4518:
4510:
4508:
4494:
4488:
4483:
4478:
4477:
4469:
4459:
4457:
4456:
4451:
4437:
4435:
4434:
4429:
4420:
4419:
4414:
4396:
4391:
4390:
4385:
4370:
4362:
4354:
4348:
4343:
4323:
4321:
4320:
4315:
4306:
4305:
4300:
4285:
4284:
4276:
4273:
4267:
4262:
4250:
4248:
4237:
4225:
4224:
4219:
4201:
4195:
4190:
4157:
4155:
4154:
4149:
4147:
4146:
4130:
4128:
4127:
4122:
4120:
4116:
4114:
4113:
4104:
4093:
4074:
4072:
4071:
4066:
4039:
4037:
4036:
4031:
4029:
4028:
3952:
3950:
3949:
3944:
3942:
3941:
3881:
3879:
3878:
3873:
3850:
3837:
3824:
3822:
3821:
3816:
3807:
3803:
3798:
3787:
3769:
3768:
3746:
3741:
3729:
3723:
3719:
3675:
3673:
3672:
3667:
3662:
3658:
3653:
3642:
3633:
3631:
3626:
3621:
3607:
3606:
3572:
3570:
3569:
3564:
3536:
3535:
3525:
3520:
3450:
3448:
3447:
3442:
3427:
3426:
3421:
3403:
3397:
3392:
3373:
3371:
3370:
3365:
3337:
3332:
3311:
3309:
3308:
3303:
3285:
3284:
3279:
3261:
3255:
3250:
3231:
3229:
3228:
3223:
3208:
3191:
3185:
3180:
3149:
3147:
3146:
3141:
3133:
3125:
3124:
3109:
3101:
3100:
3064:
3062:
3061:
3056:
3048:
3047:
3020:
3019:
2997:
2995:
2994:
2989:
2984:
2983:
2976:
2975:
2949:
2948:
2941:
2940:
2919:
2917:
2916:
2911:
2909:
2908:
2893:
2892:
2876:
2866:
2865:
2864:
2841:
2840:
2833:
2832:
2818:
2817:
2810:
2809:
2794:
2772:
2770:
2769:
2764:
2762:
2761:
2739:
2737:
2736:
2731:
2723:
2722:
2715:
2714:
2697:
2696:
2689:
2688:
2671:
2670:
2663:
2662:
2645:
2644:
2643:
2642:
2625:
2624:
2623:
2622:
2605:
2604:
2573:
2571:
2570:
2565:
2539:
2538:
2528:
2527:
2511:
2506:
2482:
2480:
2479:
2474:
2469:
2468:
2446:
2445:
2424:
2423:
2407:
2405:
2404:
2399:
2373:
2372:
2362:
2361:
2345:
2340:
2316:
2314:
2313:
2308:
2303:
2302:
2280:
2279:
2258:
2257:
2241:
2239:
2238:
2233:
2231:
2230:
2229:
2213:
2212:
2187:
2185:
2184:
2179:
2177:
2176:
2175:
2159:
2158:
2133:
2131:
2130:
2125:
2123:
2122:
2107:
2106:
2094:
2093:
2059:sampling theorem
2054:
2052:
2051:
2046:
2041:
2040:
2022:
2021:
2009:
2008:
1968:
1966:
1965:
1960:
1952:
1951:
1936:
1935:
1923:
1922:
1892:
1890:
1889:
1884:
1879:
1871:
1870:
1852:
1851:
1836:
1835:
1820:
1819:
1807:
1806:
1769:
1767:
1766:
1761:
1759:
1758:
1742:
1740:
1739:
1734:
1732:
1731:
1715:
1713:
1712:
1707:
1690:
1689:
1671:
1670:
1666:
1638:
1637:
1622:
1619:
1611:
1597:
1596:
1569:
1568:
1553:
1551:
1550:
1545:
1531:
1530:
1512:
1511:
1507:
1479:
1478:
1463:
1460:
1452:
1438:
1437:
1410:
1409:
1325:
1323:
1322:
1317:
1312:
1292:
1291:
1266:
1264:
1263:
1258:
1247:
1246:
1225:
1224:
1198:
1197:
1180:
1179:
1135:
1133:
1132:
1127:
1122:
1118:
1116:
1115:
1106:
1105:
1104:
1082:
1073:
1070:
1069:
1060:
1056:
1042:
1041:
957:
955:
954:
949:
937:
927:
926:
898:
897:
896:
880:
879:
828:
827:
805:
803:
802:
797:
779:
778:
736:
735:
723:
722:
721:
699:
698:
644:
642:
641:
636:
631:
627:
622:
611:
602:
596:
592:
578:
577:
530:
529:
512:
511:
494:
493:
486:
484:
483:
478:
476:
474:
466:
422:
252:
245:
241:
238:
232:
201:
193:
10757:
10756:
10752:
10751:
10750:
10748:
10747:
10746:
10722:
10721:
10720:
10715:
10678:
10649:
10611:
10548:
10534:quality control
10501:
10483:Clinical trials
10460:
10435:
10419:
10407:Hazard function
10401:
10355:
10317:
10301:
10264:
10260:BreuschâGodfrey
10248:
10225:
10165:
10140:Factor analysis
10086:
10067:Graphical model
10039:
10006:
9973:
9959:
9939:
9893:
9860:
9822:
9785:
9784:
9753:
9697:
9684:
9676:
9668:
9652:
9637:
9616:Rank statistics
9610:
9589:Model selection
9577:
9535:Goodness of fit
9529:
9506:
9480:
9452:
9405:
9350:
9339:Median unbiased
9267:
9178:
9111:Order statistic
9073:
9052:
9019:
8993:
8945:
8900:
8843:
8841:Data collection
8822:
8734:
8689:
8663:
8641:
8601:
8553:
8470:Continuous data
8460:
8447:
8429:
8424:
8387:
8385:
8382:Quanta Magazine
8376:
8297:
8290:
8279:
8273:
8270:
8251:
8242:This section's
8238:
8234:
8227:
8215:
8213:
8210:Quanta Magazine
8204:
8196:
8194:
8187:
8075:Stéphane Mallat
8011:Gerald Kaiser,
7943:
7941:Further reading
7938:
7926:
7922:
7911:
7907:
7846:
7842:
7789:
7785:
7729:
7723:
7719:
7688:
7684:
7676:
7672:
7667:
7663:
7626:
7622:
7571:
7567:
7528:
7524:
7492:
7488:
7445:
7441:
7400:
7396:
7390:
7386:
7377:
7373:
7342:
7338:
7322:, A. Averbuch,
7317:
7313:
7299:
7295:
7286:
7282:
7263:Ultramicroscopy
7259:
7255:
7239:
7235:
7219:
7215:
7208:
7200:. p. 147.
7188:
7184:
7176:
7129:
7123:
7119:
7112:
7092:
7088:
7057:
7053:
7026:
7022:
7015:
7007:. p. 355.
6995:
6991:
6981:
6979:
6963:
6959:
6950:
6948:
6938:
6934:
6921:
6920:
6916:
6893:(92): 171â178.
6884:
6878:
6874:
6866:
6862:
6857:
6853:
6806:
6802:
6771:
6767:
6756:
6752:
6740:
6736:
6724:
6720:
6708:
6704:
6692:
6688:
6657:
6653:
6648:
6644:
6640:
6520:
6507:Shannon wavelet
6488:
6470:Shannon wavelet
6465:Poisson wavelet
6441:
6436:
6413:Mathieu wavelet
6363:
6358:
6341:
6315:
6314:
6297:
6296:
6294:
6291:
6290:
6270:
6265:
6259:
6256:
6255:
6238:
6233:
6227:
6224:
6223:
6198:
6195:
6194:
6154:
6131:
6130:
6128:
6125:
6124:
6104:
6099:
6093:
6090:
6089:
6072:
6067:
6061:
6058:
6057:
6037:
6032:
6012:
6011:
5984:
5979:
5959:
5958:
5941:
5938:
5937:
5936:Assume a prior
5918:
5915:
5914:
5898:
5895:
5894:
5874:
5871:
5870:
5845:
5841:
5825:
5824:
5807:
5804:
5803:
5787:
5784:
5783:
5760:
5756:
5748:
5745:
5744:
5724:
5720:
5712:
5709:
5708:
5676:
5672:
5660:
5656:
5644:
5640:
5632:
5629:
5628:
5612:
5609:
5608:
5583:
5579:
5563:
5562:
5548:
5545:
5544:
5528:
5525:
5524:
5508:
5505:
5504:
5488:
5485:
5484:
5456:
5453:
5452:
5441:
5425:computer vision
5305:
5247:signal analysis
5239:
5207:crystal defects
5173:
5069:
5063:
5033:Stéphane Mallat
5002:First wavelet (
4999:
4928:Stéphane Mallat
4885:
4862:
4828:
4798:
4790:
4774:Shannon wavelet
4770:compact support
4760: log
4681:
4678:
4677:
4654:
4650:
4648:
4645:
4644:
4617:
4613:
4602:
4599:
4598:
4572:
4567:
4566:
4546:
4545:
4540:
4534:
4529:
4528:
4514:
4498:
4493:
4484:
4479:
4468:
4467:
4464:
4461:
4460:
4445:
4442:
4441:
4415:
4410:
4409:
4392:
4386:
4381:
4380:
4366:
4353:
4344:
4339:
4333:
4330:
4329:
4301:
4296:
4295:
4275:
4274:
4269:
4263:
4255:
4241:
4236:
4220:
4215:
4214:
4197:
4191:
4183:
4171:
4168:
4167:
4142:
4138:
4136:
4133:
4132:
4109:
4105:
4094:
4092:
4088:
4080:
4077:
4076:
4045:
4042:
4041:
4012:
4008:
3973:
3970:
3969:
3925:
3921:
3904:
3901:
3900:
3889:
3858:
3855:
3854:
3845:
3839:
3832:
3826:
3788:
3786:
3782:
3752:
3748:
3742:
3734:
3718:
3716:
3713:
3712:
3692:
3643:
3641:
3637:
3625:
3620:
3596:
3592:
3590:
3587:
3586:
3531:
3527:
3521:
3513:
3507:
3504:
3503:
3422:
3417:
3416:
3399:
3393:
3385:
3379:
3376:
3375:
3333:
3325:
3319:
3316:
3315:
3280:
3275:
3274:
3257:
3251:
3243:
3237:
3234:
3233:
3204:
3187:
3181:
3173:
3167:
3164:
3163:
3129:
3120:
3116:
3105:
3096:
3092:
3090:
3087:
3086:
3079:
3070:
3037:
3033:
3009:
3005:
3003:
3000:
2999:
2971:
2967:
2966:
2962:
2936:
2932:
2931:
2927:
2925:
2922:
2921:
2898:
2894:
2882:
2878:
2872:
2860:
2856:
2849:
2828:
2824:
2823:
2819:
2805:
2801:
2800:
2796:
2790:
2778:
2775:
2774:
2757:
2753:
2745:
2742:
2741:
2710:
2706:
2705:
2701:
2684:
2680:
2679:
2675:
2658:
2654:
2653:
2649:
2638:
2634:
2633:
2629:
2618:
2614:
2613:
2609:
2600:
2596:
2594:
2591:
2590:
2534:
2530:
2523:
2516:
2505:
2488:
2485:
2484:
2455:
2451:
2435:
2431:
2419:
2415:
2413:
2410:
2409:
2368:
2364:
2357:
2350:
2339:
2322:
2319:
2318:
2289:
2285:
2269:
2265:
2253:
2249:
2247:
2244:
2243:
2225:
2218:
2214:
2208:
2204:
2193:
2190:
2189:
2171:
2164:
2160:
2154:
2150:
2139:
2136:
2135:
2115:
2111:
2102:
2098:
2089:
2085:
2083:
2080:
2079:
2073:
2066:
2030:
2026:
2017:
2013:
2004:
2000:
1998:
1995:
1994:
1992:
1981:
1974:
1944:
1940:
1931:
1927:
1918:
1914:
1906:
1903:
1902:
1875:
1866:
1862:
1844:
1840:
1828:
1824:
1815:
1811:
1802:
1798:
1778:
1775:
1774:
1754:
1750:
1748:
1745:
1744:
1727:
1723:
1721:
1718:
1717:
1682:
1678:
1662:
1655:
1651:
1627:
1623:
1618:
1607:
1586:
1582:
1564:
1560:
1558:
1555:
1554:
1523:
1519:
1503:
1496:
1492:
1468:
1464:
1459:
1448:
1427:
1423:
1405:
1401:
1399:
1396:
1395:
1344:
1308:
1281:
1277:
1272:
1269:
1268:
1236:
1232:
1214:
1210:
1193:
1186:
1175:
1168:
1147:
1144:
1143:
1111:
1107:
1100:
1096:
1083:
1081:
1077:
1065:
1061:
1055:
1031:
1027:
1025:
1022:
1021:
981:
968:of the signal.
916:
912:
911:
892:
891:
887:
869:
865:
823:
819:
814:
811:
810:
768:
764:
731:
727:
717:
716:
712:
694:
690:
688:
685:
684:
667:
612:
610:
606:
591:
567:
563:
561:
558:
557:
467:
423:
421:
360:
357:
356:
314:
265:continuous-time
253:
242:
236:
233:
218:
202:
191:
163:
120:coherent states
104:basis functions
54:Seismic wavelet
24:
17:
12:
11:
5:
10755:
10745:
10744:
10739:
10734:
10717:
10716:
10714:
10713:
10701:
10689:
10675:
10662:
10659:
10658:
10655:
10654:
10651:
10650:
10648:
10647:
10642:
10637:
10632:
10627:
10621:
10619:
10613:
10612:
10610:
10609:
10604:
10599:
10594:
10589:
10584:
10579:
10574:
10569:
10564:
10558:
10556:
10550:
10549:
10547:
10546:
10541:
10536:
10527:
10522:
10517:
10511:
10509:
10503:
10502:
10500:
10499:
10494:
10489:
10480:
10478:Bioinformatics
10474:
10472:
10462:
10461:
10449:
10448:
10445:
10444:
10441:
10440:
10437:
10436:
10434:
10433:
10427:
10425:
10421:
10420:
10418:
10417:
10411:
10409:
10403:
10402:
10400:
10399:
10394:
10389:
10384:
10378:
10376:
10367:
10361:
10360:
10357:
10356:
10354:
10353:
10348:
10343:
10338:
10333:
10327:
10325:
10319:
10318:
10316:
10315:
10310:
10305:
10297:
10292:
10287:
10286:
10285:
10283:partial (PACF)
10274:
10272:
10266:
10265:
10263:
10262:
10257:
10252:
10244:
10239:
10233:
10231:
10230:Specific tests
10227:
10226:
10224:
10223:
10218:
10213:
10208:
10203:
10198:
10193:
10188:
10182:
10180:
10173:
10167:
10166:
10164:
10163:
10162:
10161:
10160:
10159:
10144:
10143:
10142:
10132:
10130:Classification
10127:
10122:
10117:
10112:
10107:
10102:
10096:
10094:
10088:
10087:
10085:
10084:
10079:
10077:McNemar's test
10074:
10069:
10064:
10059:
10053:
10051:
10041:
10040:
10016:
10015:
10012:
10011:
10008:
10007:
10005:
10004:
9999:
9994:
9989:
9983:
9981:
9975:
9974:
9972:
9971:
9955:
9949:
9947:
9941:
9940:
9938:
9937:
9932:
9927:
9922:
9917:
9915:Semiparametric
9912:
9907:
9901:
9899:
9895:
9894:
9892:
9891:
9886:
9881:
9876:
9870:
9868:
9862:
9861:
9859:
9858:
9853:
9848:
9843:
9838:
9832:
9830:
9824:
9823:
9821:
9820:
9815:
9810:
9805:
9799:
9797:
9787:
9786:
9783:
9782:
9777:
9771:
9763:
9762:
9759:
9758:
9755:
9754:
9752:
9751:
9750:
9749:
9739:
9734:
9729:
9728:
9727:
9722:
9711:
9709:
9703:
9702:
9699:
9698:
9696:
9695:
9690:
9689:
9688:
9680:
9672:
9656:
9653:(MannâWhitney)
9648:
9647:
9646:
9633:
9632:
9631:
9620:
9618:
9612:
9611:
9609:
9608:
9607:
9606:
9601:
9596:
9586:
9581:
9578:(ShapiroâWilk)
9573:
9568:
9563:
9558:
9553:
9545:
9539:
9537:
9531:
9530:
9528:
9527:
9519:
9510:
9498:
9492:
9490:Specific tests
9486:
9485:
9482:
9481:
9479:
9478:
9473:
9468:
9462:
9460:
9454:
9453:
9451:
9450:
9445:
9444:
9443:
9433:
9432:
9431:
9421:
9415:
9413:
9407:
9406:
9404:
9403:
9402:
9401:
9396:
9386:
9381:
9376:
9371:
9366:
9360:
9358:
9352:
9351:
9349:
9348:
9343:
9342:
9341:
9336:
9335:
9334:
9329:
9314:
9313:
9312:
9307:
9302:
9297:
9286:
9284:
9275:
9269:
9268:
9266:
9265:
9260:
9255:
9254:
9253:
9243:
9238:
9237:
9236:
9226:
9225:
9224:
9219:
9214:
9204:
9199:
9194:
9193:
9192:
9187:
9182:
9166:
9165:
9164:
9159:
9154:
9144:
9143:
9142:
9137:
9127:
9126:
9125:
9115:
9114:
9113:
9103:
9098:
9093:
9087:
9085:
9075:
9074:
9062:
9061:
9058:
9057:
9054:
9053:
9051:
9050:
9045:
9040:
9035:
9029:
9027:
9021:
9020:
9018:
9017:
9012:
9007:
9001:
8999:
8995:
8994:
8992:
8991:
8986:
8981:
8976:
8971:
8966:
8961:
8955:
8953:
8947:
8946:
8944:
8943:
8941:Standard error
8938:
8933:
8928:
8927:
8926:
8921:
8910:
8908:
8902:
8901:
8899:
8898:
8893:
8888:
8883:
8878:
8873:
8871:Optimal design
8868:
8863:
8857:
8855:
8845:
8844:
8832:
8831:
8828:
8827:
8824:
8823:
8821:
8820:
8815:
8810:
8805:
8800:
8795:
8790:
8785:
8780:
8775:
8770:
8765:
8760:
8755:
8750:
8744:
8742:
8736:
8735:
8733:
8732:
8727:
8726:
8725:
8720:
8710:
8705:
8699:
8697:
8691:
8690:
8688:
8687:
8682:
8677:
8671:
8669:
8668:Summary tables
8665:
8664:
8662:
8661:
8655:
8653:
8647:
8646:
8643:
8642:
8640:
8639:
8638:
8637:
8632:
8627:
8617:
8611:
8609:
8603:
8602:
8600:
8599:
8594:
8589:
8584:
8579:
8574:
8569:
8563:
8561:
8555:
8554:
8552:
8551:
8546:
8541:
8540:
8539:
8534:
8529:
8524:
8519:
8514:
8509:
8504:
8502:Contraharmonic
8499:
8494:
8483:
8481:
8472:
8462:
8461:
8449:
8448:
8446:
8445:
8440:
8434:
8431:
8430:
8423:
8422:
8415:
8408:
8400:
8394:
8393:
8374:
8368:
8362:
8356:
8346:
8340:
8334:
8329:
8323:
8318:
8313:
8292:
8291:
8246:external links
8241:
8239:
8232:
8226:
8225:External links
8223:
8222:
8221:
8202:
8185:
8168:
8146:
8135:
8116:
8101:
8086:
8072:
8050:
8039:
8024:
8009:
7991:
7973:
7955:
7942:
7939:
7937:
7936:
7929:Gabor Wavelets
7920:
7913:Matlab Toolbox
7905:
7840:
7803:(4): 599â611.
7783:
7717:
7698:(5): 1554â72.
7682:
7670:
7661:
7620:
7583:(12): 122004.
7565:
7522:
7486:
7439:
7394:
7384:
7371:
7336:
7318:A. G. Flesia,
7311:
7293:
7280:
7269:(3): 131â146.
7253:
7233:
7213:
7206:
7182:
7179:on 2019-10-13.
7117:
7110:
7086:
7067:(3): 243â250.
7051:
7020:
7013:
7005:Academic Press
6989:
6957:
6932:
6914:
6872:
6860:
6851:
6820:(1â2): 21â59.
6800:
6765:
6750:
6734:
6718:
6702:
6686:
6667:(4): 769â792.
6651:
6641:
6639:
6636:
6635:
6634:
6631:Ultra wideband
6628:
6623:
6618:
6613:
6608:
6603:
6598:
6593:
6588:
6586:Morlet wavelet
6583:
6577:
6572:
6566:
6561:
6556:
6551:
6546:
6541:
6536:
6534:Digital cinema
6531:
6526:
6519:
6516:
6515:
6514:
6509:
6504:
6502:Morlet wavelet
6499:
6494:
6487:
6486:Complex-valued
6484:
6483:
6482:
6477:
6475:Spline wavelet
6472:
6467:
6462:
6457:
6452:
6447:
6440:
6437:
6435:
6432:
6431:
6430:
6425:
6420:
6415:
6410:
6405:
6399:
6393:
6387:
6381:
6376:
6374:Morlet wavelet
6372:Moore Wavelet
6370:
6362:
6359:
6357:
6354:
6340:
6337:
6322:
6319:
6313:
6310:
6304:
6301:
6273:
6268:
6264:
6241:
6236:
6232:
6211:
6208:
6205:
6202:
6182:
6179:
6176:
6173:
6170:
6167:
6164:
6161:
6157:
6153:
6150:
6147:
6144:
6138:
6135:
6107:
6102:
6098:
6075:
6070:
6066:
6045:
6040:
6035:
6031:
6026:
6023:
6020:
6015:
6010:
6007:
6004:
6001:
5998:
5995:
5992:
5987:
5982:
5978:
5973:
5970:
5967:
5962:
5957:
5951:
5945:
5922:
5902:
5891:Gaussian noise
5878:
5856:
5853:
5848:
5844:
5839:
5836:
5833:
5828:
5817:
5811:
5791:
5768:
5763:
5759:
5755:
5752:
5732:
5727:
5723:
5719:
5716:
5696:
5693:
5690:
5687:
5684:
5679:
5675:
5671:
5668:
5663:
5659:
5655:
5652:
5647:
5643:
5639:
5636:
5616:
5594:
5591:
5586:
5582:
5577:
5574:
5571:
5566:
5558:
5552:
5532:
5512:
5492:
5472:
5469:
5466:
5463:
5460:
5440:
5437:
5355:localisation,
5353:density-matrix
5343:calculations,
5304:
5301:
5260:(see types of
5238:
5235:
5172:
5169:
5168:
5167:
5161:
5155:
5149:
5143:
5137:Lifting scheme
5134:
5128:
5122:
5065:Main article:
5062:
5059:
5058:
5057:
5051:
5041:Ronald Coifman
5025:
5023:Alex Grossmann
5011:
5004:Haar's wavelet
4998:
4995:
4991:digital cinema
4912:Alex Grossmann
4884:
4881:
4871:For instance,
4861:
4858:
4827:
4824:
4808:and sum 1. In
4797:
4796:Scaling filter
4794:
4789:
4786:
4694:
4691:
4688:
4685:
4665:
4662:
4657:
4653:
4628:
4625:
4620:
4616:
4612:
4609:
4606:
4584:
4581:
4575:
4570:
4565:
4562:
4559:
4553:
4550:
4543:
4537:
4532:
4527:
4524:
4521:
4517:
4513:
4507:
4504:
4501:
4497:
4492:
4487:
4482:
4475:
4472:
4449:
4427:
4424:
4418:
4413:
4408:
4405:
4402:
4399:
4395:
4389:
4384:
4379:
4376:
4373:
4369:
4365:
4360:
4357:
4352:
4347:
4342:
4338:
4313:
4310:
4304:
4299:
4294:
4291:
4288:
4282:
4279:
4272:
4266:
4261:
4258:
4254:
4247:
4244:
4240:
4235:
4232:
4229:
4223:
4218:
4213:
4210:
4207:
4204:
4200:
4194:
4189:
4186:
4182:
4178:
4175:
4145:
4141:
4119:
4112:
4108:
4103:
4100:
4097:
4091:
4087:
4084:
4064:
4061:
4058:
4055:
4052:
4049:
4027:
4024:
4021:
4018:
4015:
4011:
4007:
4004:
4001:
3998:
3995:
3992:
3989:
3986:
3983:
3980:
3977:
3940:
3937:
3934:
3931:
3928:
3924:
3920:
3917:
3914:
3911:
3908:
3888:
3885:
3884:
3883:
3871:
3868:
3865:
3862:
3852:
3843:
3830:
3814:
3811:
3806:
3801:
3797:
3794:
3791:
3785:
3781:
3778:
3775:
3772:
3767:
3764:
3761:
3758:
3755:
3751:
3745:
3740:
3737:
3733:
3726:
3722:
3690:
3665:
3661:
3656:
3652:
3649:
3646:
3640:
3636:
3629:
3624:
3619:
3616:
3613:
3610:
3605:
3602:
3599:
3595:
3562:
3559:
3556:
3553:
3549:
3546:
3543:
3540:
3534:
3530:
3524:
3519:
3516:
3512:
3471:wavelet series
3440:
3437:
3434:
3431:
3425:
3420:
3415:
3412:
3409:
3406:
3402:
3396:
3391:
3388:
3384:
3363:
3360:
3357:
3354:
3350:
3347:
3344:
3341:
3336:
3331:
3328:
3324:
3301:
3298:
3295:
3292:
3289:
3283:
3278:
3273:
3270:
3267:
3264:
3260:
3254:
3249:
3246:
3242:
3221:
3218:
3215:
3212:
3207:
3203:
3200:
3197:
3194:
3190:
3184:
3179:
3176:
3172:
3139:
3136:
3132:
3128:
3123:
3119:
3115:
3112:
3108:
3104:
3099:
3095:
3078:
3077:Mother wavelet
3075:
3069:
3066:
3054:
3051:
3046:
3043:
3040:
3036:
3032:
3029:
3026:
3023:
3018:
3015:
3012:
3008:
2987:
2982:
2979:
2974:
2970:
2965:
2961:
2958:
2955:
2952:
2947:
2944:
2939:
2935:
2930:
2907:
2904:
2901:
2897:
2891:
2888:
2885:
2881:
2875:
2871:
2863:
2859:
2855:
2852:
2848:
2844:
2839:
2836:
2831:
2827:
2822:
2816:
2813:
2808:
2804:
2799:
2793:
2789:
2785:
2782:
2760:
2756:
2752:
2749:
2729:
2726:
2721:
2718:
2713:
2709:
2704:
2700:
2695:
2692:
2687:
2683:
2678:
2674:
2669:
2666:
2661:
2657:
2652:
2648:
2641:
2637:
2632:
2628:
2621:
2617:
2612:
2608:
2603:
2599:
2563:
2560:
2557:
2554:
2551:
2548:
2545:
2542:
2537:
2533:
2526:
2522:
2519:
2515:
2509:
2504:
2501:
2498:
2495:
2492:
2472:
2467:
2464:
2461:
2458:
2454:
2449:
2444:
2441:
2438:
2434:
2430:
2427:
2422:
2418:
2397:
2394:
2391:
2388:
2385:
2382:
2379:
2376:
2371:
2367:
2360:
2356:
2353:
2349:
2343:
2338:
2335:
2332:
2329:
2326:
2306:
2301:
2298:
2295:
2292:
2288:
2283:
2278:
2275:
2272:
2268:
2264:
2261:
2256:
2252:
2228:
2224:
2221:
2217:
2211:
2207:
2203:
2200:
2197:
2174:
2170:
2167:
2163:
2157:
2153:
2149:
2146:
2143:
2121:
2118:
2114:
2110:
2105:
2101:
2097:
2092:
2088:
2071:
2064:
2044:
2039:
2036:
2033:
2029:
2025:
2020:
2016:
2012:
2007:
2003:
1987:
1979:
1972:
1958:
1955:
1950:
1947:
1943:
1939:
1934:
1930:
1926:
1921:
1917:
1913:
1910:
1882:
1878:
1874:
1869:
1865:
1861:
1858:
1855:
1850:
1847:
1843:
1839:
1834:
1831:
1827:
1823:
1818:
1814:
1810:
1805:
1801:
1797:
1794:
1791:
1788:
1785:
1782:
1757:
1753:
1730:
1726:
1705:
1702:
1699:
1696:
1693:
1688:
1685:
1681:
1677:
1674:
1669:
1665:
1661:
1658:
1654:
1650:
1647:
1644:
1641:
1636:
1633:
1630:
1626:
1617:
1614:
1610:
1606:
1603:
1600:
1595:
1592:
1589:
1585:
1581:
1578:
1575:
1572:
1567:
1563:
1543:
1540:
1537:
1534:
1529:
1526:
1522:
1518:
1515:
1510:
1506:
1502:
1499:
1495:
1491:
1488:
1485:
1482:
1477:
1474:
1471:
1467:
1458:
1455:
1451:
1447:
1444:
1441:
1436:
1433:
1430:
1426:
1422:
1419:
1416:
1413:
1408:
1404:
1365:father wavelet
1343:
1340:
1315:
1311:
1307:
1304:
1301:
1298:
1295:
1290:
1287:
1284:
1280:
1276:
1256:
1253:
1250:
1245:
1242:
1239:
1235:
1231:
1228:
1223:
1220:
1217:
1213:
1208:
1205:
1202:
1196:
1192:
1189:
1185:
1178:
1174:
1171:
1167:
1163:
1160:
1157:
1154:
1151:
1125:
1121:
1114:
1110:
1103:
1099:
1095:
1092:
1089:
1086:
1080:
1076:
1068:
1064:
1059:
1054:
1051:
1048:
1045:
1040:
1037:
1034:
1030:
1018:child wavelets
980:
977:
947:
944:
941:
936:
933:
930:
925:
922:
919:
915:
910:
907:
904:
901:
895:
890:
886:
883:
878:
875:
872:
868:
864:
861:
858:
855:
852:
849:
846:
843:
840:
837:
834:
831:
826:
822:
818:
795:
792:
788:
785:
782:
777:
774:
771:
767:
763:
760:
757:
754:
751:
748:
745:
742:
739:
734:
730:
726:
720:
715:
711:
708:
705:
702:
697:
693:
665:
634:
630:
625:
621:
618:
615:
609:
605:
599:
595:
590:
587:
584:
581:
576:
573:
570:
566:
554:child wavelets
544:
543:
526:
525:
508:
507:
473:
470:
465:
462:
459:
456:
453:
450:
447:
444:
441:
438:
435:
432:
429:
426:
420:
417:
414:
411:
408:
405:
401:
398:
395:
392:
389:
386:
383:
379:
376:
373:
370:
367:
364:
353:mother wavelet
327:function space
313:
310:
255:
254:
205:
203:
196:
190:
189:Wavelet theory
187:
183:Alex Grossmann
162:
159:
88:wavelet series
15:
9:
6:
4:
3:
2:
10754:
10743:
10740:
10738:
10735:
10733:
10730:
10729:
10727:
10712:
10711:
10702:
10700:
10699:
10690:
10688:
10687:
10682:
10676:
10674:
10673:
10664:
10663:
10660:
10646:
10643:
10641:
10640:Geostatistics
10638:
10636:
10633:
10631:
10628:
10626:
10623:
10622:
10620:
10618:
10614:
10608:
10607:Psychometrics
10605:
10603:
10600:
10598:
10595:
10593:
10590:
10588:
10585:
10583:
10580:
10578:
10575:
10573:
10570:
10568:
10565:
10563:
10560:
10559:
10557:
10555:
10551:
10545:
10542:
10540:
10537:
10535:
10531:
10528:
10526:
10523:
10521:
10518:
10516:
10513:
10512:
10510:
10508:
10504:
10498:
10495:
10493:
10490:
10488:
10484:
10481:
10479:
10476:
10475:
10473:
10471:
10470:Biostatistics
10467:
10463:
10459:
10454:
10450:
10432:
10431:Log-rank test
10429:
10428:
10426:
10422:
10416:
10413:
10412:
10410:
10408:
10404:
10398:
10395:
10393:
10390:
10388:
10385:
10383:
10380:
10379:
10377:
10375:
10371:
10368:
10366:
10362:
10352:
10349:
10347:
10344:
10342:
10339:
10337:
10334:
10332:
10329:
10328:
10326:
10324:
10320:
10314:
10311:
10309:
10306:
10304:
10302:(BoxâJenkins)
10298:
10296:
10293:
10291:
10288:
10284:
10281:
10280:
10279:
10276:
10275:
10273:
10271:
10267:
10261:
10258:
10256:
10255:DurbinâWatson
10253:
10251:
10245:
10243:
10240:
10238:
10237:DickeyâFuller
10235:
10234:
10232:
10228:
10222:
10219:
10217:
10214:
10212:
10211:Cointegration
10209:
10207:
10204:
10202:
10199:
10197:
10194:
10192:
10189:
10187:
10186:Decomposition
10184:
10183:
10181:
10177:
10174:
10172:
10168:
10158:
10155:
10154:
10153:
10150:
10149:
10148:
10145:
10141:
10138:
10137:
10136:
10133:
10131:
10128:
10126:
10123:
10121:
10118:
10116:
10113:
10111:
10108:
10106:
10103:
10101:
10098:
10097:
10095:
10093:
10089:
10083:
10080:
10078:
10075:
10073:
10070:
10068:
10065:
10063:
10060:
10058:
10057:Cohen's kappa
10055:
10054:
10052:
10050:
10046:
10042:
10038:
10034:
10030:
10026:
10021:
10017:
10003:
10000:
9998:
9995:
9993:
9990:
9988:
9985:
9984:
9982:
9980:
9976:
9970:
9966:
9962:
9956:
9954:
9951:
9950:
9948:
9946:
9942:
9936:
9933:
9931:
9928:
9926:
9923:
9921:
9918:
9916:
9913:
9911:
9910:Nonparametric
9908:
9906:
9903:
9902:
9900:
9896:
9890:
9887:
9885:
9882:
9880:
9877:
9875:
9872:
9871:
9869:
9867:
9863:
9857:
9854:
9852:
9849:
9847:
9844:
9842:
9839:
9837:
9834:
9833:
9831:
9829:
9825:
9819:
9816:
9814:
9811:
9809:
9806:
9804:
9801:
9800:
9798:
9796:
9792:
9788:
9781:
9778:
9776:
9773:
9772:
9768:
9764:
9748:
9745:
9744:
9743:
9740:
9738:
9735:
9733:
9730:
9726:
9723:
9721:
9718:
9717:
9716:
9713:
9712:
9710:
9708:
9704:
9694:
9691:
9687:
9681:
9679:
9673:
9671:
9665:
9664:
9663:
9660:
9659:Nonparametric
9657:
9655:
9649:
9645:
9642:
9641:
9640:
9634:
9630:
9629:Sample median
9627:
9626:
9625:
9622:
9621:
9619:
9617:
9613:
9605:
9602:
9600:
9597:
9595:
9592:
9591:
9590:
9587:
9585:
9582:
9580:
9574:
9572:
9569:
9567:
9564:
9562:
9559:
9557:
9554:
9552:
9550:
9546:
9544:
9541:
9540:
9538:
9536:
9532:
9526:
9524:
9520:
9518:
9516:
9511:
9509:
9504:
9500:
9499:
9496:
9493:
9491:
9487:
9477:
9474:
9472:
9469:
9467:
9464:
9463:
9461:
9459:
9455:
9449:
9446:
9442:
9439:
9438:
9437:
9434:
9430:
9427:
9426:
9425:
9422:
9420:
9417:
9416:
9414:
9412:
9408:
9400:
9397:
9395:
9392:
9391:
9390:
9387:
9385:
9382:
9380:
9377:
9375:
9372:
9370:
9367:
9365:
9362:
9361:
9359:
9357:
9353:
9347:
9344:
9340:
9337:
9333:
9330:
9328:
9325:
9324:
9323:
9320:
9319:
9318:
9315:
9311:
9308:
9306:
9303:
9301:
9298:
9296:
9293:
9292:
9291:
9288:
9287:
9285:
9283:
9279:
9276:
9274:
9270:
9264:
9261:
9259:
9256:
9252:
9249:
9248:
9247:
9244:
9242:
9239:
9235:
9234:loss function
9232:
9231:
9230:
9227:
9223:
9220:
9218:
9215:
9213:
9210:
9209:
9208:
9205:
9203:
9200:
9198:
9195:
9191:
9188:
9186:
9183:
9181:
9175:
9172:
9171:
9170:
9167:
9163:
9160:
9158:
9155:
9153:
9150:
9149:
9148:
9145:
9141:
9138:
9136:
9133:
9132:
9131:
9128:
9124:
9121:
9120:
9119:
9116:
9112:
9109:
9108:
9107:
9104:
9102:
9099:
9097:
9094:
9092:
9089:
9088:
9086:
9084:
9080:
9076:
9072:
9067:
9063:
9049:
9046:
9044:
9041:
9039:
9036:
9034:
9031:
9030:
9028:
9026:
9022:
9016:
9013:
9011:
9008:
9006:
9003:
9002:
9000:
8996:
8990:
8987:
8985:
8982:
8980:
8977:
8975:
8972:
8970:
8967:
8965:
8962:
8960:
8957:
8956:
8954:
8952:
8948:
8942:
8939:
8937:
8936:Questionnaire
8934:
8932:
8929:
8925:
8922:
8920:
8917:
8916:
8915:
8912:
8911:
8909:
8907:
8903:
8897:
8894:
8892:
8889:
8887:
8884:
8882:
8879:
8877:
8874:
8872:
8869:
8867:
8864:
8862:
8859:
8858:
8856:
8854:
8850:
8846:
8842:
8837:
8833:
8819:
8816:
8814:
8811:
8809:
8806:
8804:
8801:
8799:
8796:
8794:
8791:
8789:
8786:
8784:
8781:
8779:
8776:
8774:
8771:
8769:
8766:
8764:
8763:Control chart
8761:
8759:
8756:
8754:
8751:
8749:
8746:
8745:
8743:
8741:
8737:
8731:
8728:
8724:
8721:
8719:
8716:
8715:
8714:
8711:
8709:
8706:
8704:
8701:
8700:
8698:
8696:
8692:
8686:
8683:
8681:
8678:
8676:
8673:
8672:
8670:
8666:
8660:
8657:
8656:
8654:
8652:
8648:
8636:
8633:
8631:
8628:
8626:
8623:
8622:
8621:
8618:
8616:
8613:
8612:
8610:
8608:
8604:
8598:
8595:
8593:
8590:
8588:
8585:
8583:
8580:
8578:
8575:
8573:
8570:
8568:
8565:
8564:
8562:
8560:
8556:
8550:
8547:
8545:
8542:
8538:
8535:
8533:
8530:
8528:
8525:
8523:
8520:
8518:
8515:
8513:
8510:
8508:
8505:
8503:
8500:
8498:
8495:
8493:
8490:
8489:
8488:
8485:
8484:
8482:
8480:
8476:
8473:
8471:
8467:
8463:
8459:
8454:
8450:
8444:
8441:
8439:
8436:
8435:
8432:
8428:
8421:
8416:
8414:
8409:
8407:
8402:
8401:
8398:
8383:
8379:
8375:
8372:
8369:
8366:
8363:
8360:
8357:
8354:
8350:
8347:
8344:
8341:
8338:
8335:
8333:
8330:
8327:
8324:
8322:
8319:
8317:
8314:
8310:
8306:
8305:
8300:
8296:
8295:
8288:
8285:
8277:
8267:
8263:
8262:inappropriate
8259:
8255:
8249:
8247:
8240:
8231:
8230:
8211:
8207:
8203:
8193:on 2011-08-11
8192:
8188:
8182:
8178:
8174:
8169:
8166:
8165:0-89871-589-X
8162:
8158:
8154:
8150:
8147:
8144:
8143:0-08-044335-4
8140:
8136:
8133:
8132:0-7503-0692-0
8129:
8125:
8121:
8117:
8114:
8113:0-12-279670-5
8110:
8106:
8102:
8099:
8098:0-521-68508-7
8095:
8091:
8087:
8084:
8083:0-12-466606-X
8080:
8076:
8073:
8070:
8066:
8062:
8061:1-56881-072-5
8058:
8054:
8051:
8048:
8047:0-13-097080-8
8044:
8040:
8037:
8036:1-56881-041-5
8033:
8029:
8025:
8022:
8021:0-8176-3711-7
8018:
8014:
8010:
8007:
8006:0-13-605718-7
8003:
7999:
7995:
7992:
7989:
7988:0-12-047140-X
7985:
7981:
7977:
7974:
7971:
7970:0-89871-274-2
7967:
7963:
7959:
7956:
7953:
7949:
7945:
7944:
7934:
7930:
7924:
7918:
7914:
7909:
7901:
7897:
7892:
7887:
7883:
7879:
7875:
7871:
7867:
7863:
7859:
7855:
7851:
7844:
7836:
7832:
7828:
7824:
7819:
7814:
7810:
7806:
7802:
7798:
7794:
7787:
7779:
7775:
7771:
7767:
7763:
7759:
7755:
7751:
7747:
7743:
7739:
7735:
7728:
7721:
7713:
7709:
7705:
7701:
7697:
7693:
7686:
7680:
7674:
7665:
7656:
7651:
7647:
7643:
7640:(1): 012032.
7639:
7635:
7631:
7624:
7616:
7612:
7608:
7604:
7600:
7596:
7591:
7586:
7582:
7578:
7577:
7569:
7561:
7557:
7553:
7549:
7545:
7541:
7537:
7533:
7532:J. Phys. Chem
7526:
7517:
7513:
7509:
7505:
7501:
7497:
7490:
7482:
7478:
7474:
7470:
7466:
7462:
7458:
7454:
7450:
7443:
7436:
7431:
7427:
7422:
7417:
7413:
7409:
7405:
7398:
7388:
7381:
7375:
7367:
7363:
7359:
7355:
7351:
7347:
7340:
7333:
7329:
7325:
7321:
7315:
7308:
7305:
7304:
7297:
7290:
7284:
7276:
7272:
7268:
7264:
7257:
7250:
7246:
7243:
7237:
7231:
7230:0-88275-376-2
7227:
7223:
7217:
7209:
7207:9780240806174
7203:
7199:
7195:
7194:
7186:
7175:
7171:
7167:
7163:
7159:
7155:
7151:
7147:
7143:
7139:
7135:
7128:
7121:
7113:
7111:9781461507994
7107:
7103:
7099:
7098:
7090:
7082:
7078:
7074:
7070:
7066:
7062:
7055:
7047:
7043:
7039:
7035:
7031:
7024:
7016:
7014:9780080922508
7010:
7006:
7002:
7001:
6993:
6978:
6974:
6973:
6968:
6961:
6947:
6943:
6936:
6928:
6924:
6918:
6910:
6906:
6901:
6896:
6892:
6891:
6883:
6876:
6870:
6864:
6855:
6847:
6843:
6838:
6833:
6828:
6823:
6819:
6815:
6811:
6804:
6796:
6792:
6788:
6784:
6780:
6776:
6769:
6761:
6754:
6748:
6744:
6738:
6732:
6728:
6722:
6716:
6715:0-12-174584-8
6712:
6706:
6700:
6699:0-521-42000-8
6696:
6690:
6682:
6678:
6674:
6670:
6666:
6662:
6655:
6646:
6642:
6632:
6629:
6627:
6624:
6622:
6619:
6617:
6614:
6612:
6609:
6607:
6604:
6602:
6599:
6597:
6594:
6592:
6589:
6587:
6584:
6581:
6578:
6576:
6573:
6570:
6567:
6565:
6562:
6560:
6557:
6555:
6552:
6550:
6547:
6545:
6542:
6540:
6537:
6535:
6532:
6530:
6527:
6525:
6522:
6521:
6513:
6510:
6508:
6505:
6503:
6500:
6498:
6495:
6493:
6490:
6489:
6481:
6478:
6476:
6473:
6471:
6468:
6466:
6463:
6461:
6458:
6456:
6455:Meyer wavelet
6453:
6451:
6448:
6446:
6443:
6442:
6429:
6426:
6424:
6421:
6419:
6416:
6414:
6411:
6409:
6406:
6403:
6400:
6397:
6394:
6391:
6388:
6385:
6382:
6380:
6377:
6375:
6371:
6368:
6365:
6364:
6353:
6350:
6346:
6336:
6317:
6311:
6308:
6299:
6287:
6271:
6266:
6262:
6239:
6234:
6230:
6206:
6200:
6180:
6174:
6168:
6165:
6159:
6155:
6151:
6145:
6142:
6133:
6121:
6105:
6100:
6096:
6073:
6068:
6064:
6038:
6033:
6029:
6024:
6021:
6005:
6002:
5999:
5993:
5985:
5980:
5976:
5971:
5968:
5955:
5949:
5943:
5934:
5920:
5900:
5892:
5876:
5867:
5851:
5846:
5842:
5837:
5834:
5815:
5809:
5789:
5780:
5766:
5761:
5757:
5753:
5750:
5730:
5725:
5721:
5717:
5714:
5694:
5691:
5688:
5685:
5682:
5677:
5673:
5669:
5666:
5661:
5657:
5653:
5650:
5645:
5641:
5637:
5634:
5614:
5605:
5589:
5584:
5580:
5575:
5572:
5556:
5550:
5530:
5510:
5490:
5470:
5467:
5464:
5461:
5458:
5445:
5436:
5434:
5430:
5426:
5422:
5421:sparse coding
5418:
5414:
5410:
5406:
5402:
5398:
5394:
5390:
5389:brain rhythms
5386:
5382:
5378:
5374:
5370:
5366:
5362:
5358:
5354:
5350:
5346:
5342:
5338:
5334:
5330:
5325:
5323:
5319:
5315:
5311:
5300:
5298:
5294:
5290:
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5259:
5255:
5250:
5248:
5244:
5234:
5230:
5228:
5224:
5220:
5216:
5215:nanostructure
5212:
5208:
5204:
5200:
5196:
5192:
5187:
5185:
5180:
5178:
5165:
5162:
5159:
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5135:
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5016:
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5009:
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4988:
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4880:
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4854:
4852:
4848:
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4623:
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3709:
3708:RestrictionïŒ
3706:
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2076:
2074:
2067:
2060:
2055:
2042:
2037:
2034:
2031:
2027:
2023:
2018:
2014:
2010:
2005:
2001:
1990:
1986:
1982:
1975:
1956:
1953:
1948:
1945:
1941:
1937:
1932:
1928:
1924:
1919:
1915:
1911:
1908:
1900:
1896:
1867:
1863:
1859:
1856:
1853:
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1845:
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1837:
1832:
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1825:
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1358:
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1337:
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1329:
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1302:
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1293:
1288:
1285:
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1251:
1243:
1240:
1237:
1233:
1229:
1221:
1218:
1215:
1211:
1206:
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1190:
1187:
1183:
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1169:
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1161:
1155:
1149:
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1119:
1112:
1108:
1101:
1097:
1093:
1090:
1087:
1084:
1078:
1074:
1066:
1062:
1057:
1052:
1046:
1038:
1035:
1032:
1028:
1019:
1015:
1011:
1007:
1003:
999:
995:
991:
987:
976:
974:
969:
967:
963:
958:
945:
942:
939:
931:
923:
920:
917:
913:
905:
899:
888:
884:
876:
873:
870:
866:
862:
859:
853:
847:
844:
841:
832:
824:
820:
816:
809:
793:
790:
783:
775:
772:
769:
765:
761:
755:
752:
749:
740:
732:
728:
724:
713:
709:
703:
695:
691:
682:
678:
673:
671:
664:
660:
656:
652:
648:
632:
628:
623:
619:
616:
613:
607:
603:
597:
593:
588:
582:
574:
571:
568:
564:
555:
551:
540:
536:
532:
531:
522:
518:
514:
513:
504:
500:
496:
495:
492:
490:
489:sinc function
471:
468:
460:
457:
451:
448:
445:
439:
436:
433:
427:
424:
418:
412:
406:
403:
399:
393:
390:
384:
381:
377:
374:
368:
362:
354:
350:
346:
341:
339:
335:
331:
328:
325:
324:
319:
309:
306:
303:
298:
294:
290:
286:
281:
278:
277:discrete-time
274:
273:discrete-time
270:
266:
262:
251:
248:
240:
237:November 2014
230:
226:
222:
216:
215:
211:
206:This section
204:
200:
195:
194:
186:
184:
180:
176:
172:
168:
158:
156:
152:
148:
144:
140:
136:
132:
128:
123:
121:
117:
116:Hilbert space
113:
109:
105:
101:
97:
93:
89:
84:
82:
77:
76:audio signals
72:
70:
65:
61:
60:middle C
52:
48:
46:
41:
37:
33:
29:
22:
10708:
10696:
10677:
10670:
10582:Econometrics
10532: /
10515:Chemometrics
10492:Epidemiology
10485: /
10458:Applications
10345:
10300:ARIMA model
10247:Q-statistic
10196:Stationarity
10092:Multivariate
10035: /
10031: /
10029:Multivariate
10027: /
9967: /
9963: /
9737:Bayes factor
9636:Signed rank
9548:
9522:
9514:
9502:
9197:Completeness
9033:Cohort study
8931:Opinion poll
8866:Missing data
8853:Study design
8808:Scatter plot
8730:Scatter plot
8723:Spearman's Ï
8685:Grouped data
8386:. Retrieved
8384:. 2021-10-13
8381:
8351:describes a
8302:
8280:
8271:
8256:by removing
8243:
8214:. Retrieved
8212:. 2021-10-13
8209:
8195:, retrieved
8191:the original
8176:
8156:
8149:Tony F. Chan
8119:
8104:
8089:
8027:
8012:
7997:
7979:
7961:
7951:
7947:
7928:
7923:
7912:
7908:
7857:
7853:
7843:
7800:
7796:
7786:
7737:
7733:
7720:
7695:
7691:
7685:
7673:
7664:
7637:
7633:
7623:
7580:
7576:Phys. Rev. D
7574:
7568:
7538:(1): 19â22.
7535:
7531:
7525:
7502:(7): 64â71.
7499:
7495:
7489:
7456:
7452:
7442:
7433:
7414:(22): 4644.
7411:
7407:
7397:
7387:
7374:
7349:
7345:
7339:
7331:
7328:D. L. Donoho
7324:E. J. Candes
7314:
7306:
7301:
7296:
7288:
7283:
7266:
7262:
7256:
7244:
7241:
7236:
7221:
7216:
7192:
7185:
7174:the original
7137:
7133:
7120:
7096:
7089:
7064:
7060:
7054:
7029:
7023:
6999:
6992:
6982:13 September
6980:. Retrieved
6970:
6960:
6949:. Retrieved
6945:
6935:
6926:
6917:
6888:
6875:
6863:
6854:
6817:
6813:
6803:
6778:
6774:
6768:
6759:
6753:
6737:
6721:
6705:
6689:
6664:
6660:
6654:
6645:
6544:Filter banks
6497:fbsp wavelet
6445:Beta wavelet
6408:Haar wavelet
6402:Binomial QMF
6342:
6288:
6122:
5935:
5868:
5781:
5606:
5450:
5345:astrophysics
5337:chaos theory
5326:
5306:
5274:
5270:
5257:
5251:
5240:
5237:Applications
5231:
5188:
5181:
5174:
5109:
5098:
5070:
5015:George Zweig
4948:
4942:(1993), and
4936:binomial QMF
4904:George Zweig
4901:
4893:Dennis Gabor
4886:
4870:
4865:
4863:
4855:
4850:
4846:
4844:
4840:
4835:
4831:
4829:
4821:
4814:
4810:biorthogonal
4805:
4799:
4791:
4781:
4777:
4772:such as the
4761:
4757:
4751:
4743:
4737:
4733:
4719:
4715:
4709:, such as a
4596:
4439:
4328:is given by
4325:
4159:
3967:
3890:
3847:
3840:
3834:
3827:
3707:
3703:
3699:affine group
3698:
3694:
3687:
3683:
3679:
3677:
3585:
3580:
3576:
3574:
3500:
3496:
3492:
3490:
3481:
3477:
3464:
3455:
3453:
3313:
3080:
3071:
2586:
2584:
2077:
2069:
2062:
2056:
1988:
1984:
1977:
1970:
1898:
1772:
1393:
1384:
1380:
1376:
1375:), and that
1372:
1368:
1364:
1353:
1335:
1331:
1139:
1137:
1017:
1013:
1009:
1005:
1001:
997:
993:
989:
982:
970:
961:
959:
807:
680:
676:
674:
669:
662:
658:
654:
650:
646:
553:
549:
547:
352:
348:
344:
342:
337:
333:
329:
322:
315:
307:
258:
243:
234:
219:Please help
207:
174:
166:
164:
147:interference
124:
108:overcomplete
85:
73:
57:
27:
25:
10710:WikiProject
10625:Cartography
10587:Jurimetrics
10539:Reliability
10270:Time domain
10249:(LjungâBox)
10171:Time-series
10049:Categorical
10033:Time-series
10025:Categorical
9960:(Bernoulli)
9795:Correlation
9775:Correlation
9571:JarqueâBera
9543:Chi-squared
9305:M-estimator
9258:Asymptotics
9202:Sufficiency
8969:Interaction
8881:Replication
8861:Effect size
8818:Violin plot
8798:Radar chart
8778:Forest plot
8768:Correlogram
8718:Kendall's Ï
7860:(1): 8808.
7740:(11): 296.
7408:Mathematics
6781:(9): 1825.
6626:Spectrogram
6606:Scale space
6439:Real-valued
5433:scale space
5401:climatology
5258:tight frame
5209:. Now that
5103:(DWTs) and
5092:and/or non-
5019:Jean Morlet
5008:Alfréd Haar
4977:algorithm.
4916:Jean Morlet
4897:Gabor atoms
4889:Alfréd Haar
539:Mexican hat
280:filterbanks
179:Jean Morlet
100:orthonormal
69:Correlation
36:oscillation
21:Wave packet
10726:Categories
10577:Demography
10295:ARMA model
10100:Regression
9677:(Friedman)
9638:(Wilcoxon)
9576:Normality
9566:Lilliefors
9513:Student's
9389:Resampling
9263:Robustness
9251:divergence
9241:Efficiency
9179:(monotone)
9174:Likelihood
9091:Population
8924:Stratified
8876:Population
8695:Dependence
8651:Count data
8582:Percentile
8559:Dispersion
8492:Arithmetic
8427:Statistics
8388:2021-10-20
8216:2021-10-20
8197:2011-08-13
7976:Ali Akansu
7590:1602.03843
7459:: 133453.
7435:filtering.
6951:2021-10-20
6661:Geophysics
6638:References
5399:analysis,
5395:analysis,
5387:analyses,
5365:turbulence
5357:seismology
5094:stationary
5082:translated
5045:Ali Akansu
5029:Yves Meyer
4932:Ali Akansu
4764:) for the
1389:Daubechies
1350:D4 wavelet
966:scaleogram
302:scaleogram
143:wavelength
114:, for the
9958:Logistic
9725:posterior
9651:Rank sum
9399:Jackknife
9394:Bootstrap
9212:Bootstrap
9147:Parameter
9096:Statistic
8891:Statistic
8803:Run chart
8788:Pie chart
8783:Histogram
8773:Fan chart
8748:Bar chart
8630:L-moments
8517:Geometric
8309:EMS Press
8274:July 2016
8258:excessive
7946:Haar A.,
7882:2045-2322
7827:1607-7946
7778:125557123
7770:1434-6028
7762:1434-6036
7615:119313566
7481:263317973
7473:0950-0618
7430:2227-7390
7366:255201598
7320:H. Hel-Or
7081:1051-8215
7046:109186495
6575:JPEG 2000
6321:~
6303:~
6263:σ
6231:σ
6201:τ
6169:τ
6137:~
6097:σ
6065:σ
6030:σ
6003:−
5977:σ
5950:∼
5843:σ
5816:∼
5581:σ
5557:∼
5341:ab initio
5293:IEEE 1901
5289:Panasonic
5254:JPEG 2000
5227:metrology
5191:darkfield
5096:signals.
5055:JPEG 2000
4993:in 2004.
4979:JPEG 2000
4951:JPEG 2000
4748:, taking
4664:∞
4661:→
4652:Δ
4624:ω
4615:Δ
4608:
4583:ω
4561:ω
4552:^
4549:ψ
4526:ξ
4523:−
4520:ω
4512:∫
4503:π
4481:ξ
4474:^
4471:σ
4448:ξ
4398:ψ
4375:−
4364:∫
4337:σ
4312:ω
4290:ω
4281:^
4278:ψ
4265:∞
4260:∞
4257:−
4253:∫
4246:π
4203:ψ
4193:∞
4188:∞
4185:−
4181:∫
4140:Δ
4107:Δ
4099:−
4086:
4057:−
4020:π
4014:−
4000:−
3976:ψ
3959:frequency
3933:π
3927:−
3907:ψ
3861:Ψ
3793:−
3780:φ
3750:φ
3744:∞
3739:∞
3736:−
3732:∫
3648:−
3635:ψ
3594:ψ
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3405:ψ
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3390:∞
3387:−
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3340:ψ
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3330:∞
3327:−
3323:∫
3297:∞
3263:ψ
3253:∞
3248:∞
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3220:∞
3193:ψ
3183:∞
3178:∞
3175:−
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3114:∩
3050:⟩
3035:ψ
3025:⟨
2986:⟩
2964:ϕ
2954:⟨
2896:ψ
2870:∑
2854:≤
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2821:ϕ
2788:∑
2751:∈
2728:⋯
2725:⊕
2717:−
2699:⊕
2691:−
2673:⊕
2665:−
2647:⊕
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2169:∈
2117:−
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2035:−
2011:⊕
1957:…
1946:−
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1695:−
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1657:−
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1498:−
1466:ϕ
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1425:ϕ
1418:
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1279:ψ
1234:ψ
1230:⋅
1227:⟩
1212:ψ
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1191:∈
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1173:∈
1166:∑
1088:−
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1029:ψ
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889:∫
882:⟩
867:ψ
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825:ψ
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762:⋅
733:ψ
714:∫
617:−
604:ψ
565:ψ
469:π
458:π
452:
446:−
437:π
428:
407:
400:−
385:
363:ψ
287:(FIR) or
208:does not
175:ondelette
165:The word
161:Etymology
153:(e.g., a
135:wavefront
64:convolved
40:amplitude
10732:Wavelets
10672:Category
10365:Survival
10242:Johansen
9965:Binomial
9920:Isotonic
9507:(normal)
9152:location
8959:Blocking
8914:Sampling
8793:QâQ plot
8758:Box plot
8740:Graphics
8635:Skewness
8625:Kurtosis
8597:Variance
8527:Heronian
8522:Harmonic
8326:Wavelets
8126:, 2002,
7900:31217490
7835:28114574
7560:19072712
7162:18237979
6846:36689001
6837:10160219
6616:Shearlet
6596:Noiselet
6529:Curvelet
6518:See also
6056:, where
5707:, where
5483:, where
5203:crystals
5090:periodic
4997:Timeline
4895:yielded
4711:Gaussian
4131:, where
3465:For the
2483:so that
2317:so that
1893:forms a
1383:= 2 and
1326:form an
992:> 1,
139:coherent
106:, or an
96:complete
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10698:Commons
10645:Kriging
10530:Process
10487:studies
10346:Wavelet
10179:General
9346:Plug-in
9140:L space
8919:Cluster
8620:Moments
8438:Outline
8311:, 2001
8252:Please
8244:use of
8167:(2005).
7915:â URL:
7891:6584743
7862:Bibcode
7805:Bibcode
7742:Bibcode
7700:Bibcode
7642:Bibcode
7595:Bibcode
7540:Bibcode
7516:2650873
7330:(2001)
7170:2765169
7142:Bibcode
6909:9720759
6783:Bibcode
6669:Bibcode
6384:Coiflet
6367:Beylkin
5397:protein
4883:History
4746:complex
1004:) with
351:), the
229:removed
214:sources
167:wavelet
110:set or
102:set of
28:wavelet
10567:Census
10157:Normal
10105:Manova
9925:Robust
9675:2-way
9667:1-way
9505:-test
9176:
8753:Biplot
8544:Median
8537:Lehmer
8479:Center
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5822:
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5560:
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5419:, and
5361:optics
5281:HD-PLC
5223:strain
5166:(FRWT)
5160:(FRFT)
5078:scaled
5010:(1909)
4738:single
4040:where
3961:. The
1363:, the
986:affine
645:where
521:Morlet
171:French
34:-like
10191:Trend
9720:prior
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9551:-test
9525:-test
9517:-test
9424:Power
9369:Pivot
9162:shape
9157:scale
8607:Shape
8587:Range
8532:Heinz
8507:Cubic
8443:Index
7931:URL:
7878:eISSN
7831:S2CID
7823:eISSN
7774:S2CID
7758:eISSN
7730:(PDF)
7679:(pdf)
7611:S2CID
7585:arXiv
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7177:(PDF)
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7042:S2CID
6972:ITU-T
6905:S2CID
6885:(PDF)
6123:Then
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5423:. In
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5148:(WPD)
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5006:) by
3825:when
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3084:space
1367:Ï in
806:with
503:Meyer
173:word
30:is a
10424:Test
9624:Sign
9476:Wald
8549:Mode
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8181:ISBN
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854:=
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848:b
845:,
842:a
839:(
836:}
833:x
830:{
821:T
817:W
794:b
791:d
787:)
784:t
781:(
776:b
773:,
770:a
759:)
756:b
753:,
750:a
747:(
744:}
741:x
738:{
729:T
725:W
719:R
710:=
707:)
704:t
701:(
696:a
692:x
681:a
677:x
670:R
666:+
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659:b
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651:b
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624:a
620:b
614:t
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589:=
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583:t
580:(
575:b
572:,
569:a
550:a
472:t
464:)
461:t
455:(
443:)
440:t
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397:)
394:t
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375:=
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349:R
347:(
345:L
338:f
334:R
332:(
330:L
323:L
250:)
244:(
239:)
235:(
231:.
217:.
23:.
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